BuyFind

Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621
BuyFind

Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

Solutions

Chapter
Section
Chapter 6.7, Problem 46E
Textbook Problem

Show that d d x 1 + tanh x 1 tanh x 4 = 1 2 e x / 2

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Chapter 6 Solutions

Calculus (MindTap Course List)
Show all chapter solutions
Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - Assume that f is a one-to-one function. a If...Ch. 6.1 - If f(x)=x5+x3+x, find f1(3) and f(f1(2)).Ch. 6.1 - If h(x)=x+x, find h1(6).Ch. 6.1 - The graph of f is given. a Why is f one-to-one? b...Ch. 6.1 - The formula C=59(F32), where F459.67, expresses...Ch. 6.1 - In the theory of relativity, the mass of a...Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find an explicit formula for f1 and use it to...Ch. 6.1 - Find an explicit formula for f1 and use it to...Ch. 6.1 - Use the given graph of f to sketch the graph of...Ch. 6.1 - Use the given graph of f to sketch the graph of...Ch. 6.1 - Let f(x)=1x2,0x1. a Find f1. How is it related to...Ch. 6.1 - Let g(x)=1x33. a Find g1. How is it related to g?...Ch. 6.1 - a Show that f is one-to-one. b Use Theorem 7 to...Ch. 6.1 - a Show that f is one-to-one. b Use Theorem 7 to...Ch. 6.1 - a Show that f is one-to-one. b Use Theorem 7 to...Ch. 6.1 - a Show that f is one-to-one. b Use Theorem 7 to...Ch. 6.1 - Find (f1)(a). f(x)=3x3+4x2+6x+5,a=5Ch. 6.1 - Find (f1)(a). f(x)=x3+3sinx+2cosx,a=2Ch. 6.1 - Find (f1)(a). f(x)=3+x2+tan(x/2),1x1,a=3Ch. 6.1 - Find (f1)(a). f(x)=x3+4x+4,a=3Ch. 6.1 - Suppose f1 is the inverse function of a...Ch. 6.1 - If g is an increasing function such that g(2)=8...Ch. 6.1 - If f(x)=3x1+t3dt, find (f1)(0).Ch. 6.1 - Suppose f1 is the inverse function of a...Ch. 6.1 - Graph the function f(x)=x3+x2+x+1 and explain why...Ch. 6.1 - Show that h(x)=sinx,x, is not one-to-one, but its...Ch. 6.1 - a If we shift a curve to the left, what happens to...Ch. 6.1 - a If f is a one-to-one, twice differentiable...Ch. 6.2 - a Write an equation that defines the exponential...Ch. 6.2 - a How is the number e defined? b What is an...Ch. 6.2 - Graph the given functions on a common screen. How...Ch. 6.2 - Graph the given functions on a common screen. How...Ch. 6.2 - Graph the given functions on a common screen. How...Ch. 6.2 - Graph the given functions on a common screen. How...Ch. 6.2 - Make a rough sketch of the graph of the function....Ch. 6.2 - Make a rough sketch of the graph of the function....Ch. 6.2 - Make a rough sketch of the graph of the function....Ch. 6.2 - Make a rough sketch of the graph of the function....Ch. 6.2 - 7-12 Make a rough sketch of the graph of the...Ch. 6.2 - 7-12 Make a rough sketch of the graph of the...Ch. 6.2 - Starting with the graph of y=ex, write the...Ch. 6.2 - Starting with the graph of y=ex, find the equation...Ch. 6.2 - Find the domain of each function. a f(x)=1ex21e1x2...Ch. 6.2 - Find the domain of each function. a g(t)=10t100b...Ch. 6.2 - 17-18 Find the exponential function f(x)=Cbx whose...Ch. 6.2 - 17-18 Find the exponential function f(x)=Cbx whose...Ch. 6.2 - Suppose the graphs of f(x)=x2 and g(x)=2x are...Ch. 6.2 - Compare the functions f(x)=x5 and g(x)=5x by...Ch. 6.2 - Compare the functions f(x)=x10 and g(x)=ex by...Ch. 6.2 - Use a graph to estimate the values of x such that...Ch. 6.2 - 23-30 Find the limit. limx(1.001)xCh. 6.2 - 23-30 Find the limit. limx(1.001)xCh. 6.2 - 23-30 Find the limit. limxe3xe3xe3x+e3xCh. 6.2 - 23-30 Find the limit. limxex2Ch. 6.2 - 23-30 Find the limit. limx2+e3/(2x)Ch. 6.2 - 23-30 Find the limit. limx2+e3/(2x)Ch. 6.2 - 23-30 Find the limit. limx(e2xcosx)Ch. 6.2 - 23-30 Find the limit. limx(/2)etanxCh. 6.2 - 31-50 Differentiate the function. f(x)=e5Ch. 6.2 - 31-50 Differentiate the function. k(r)=er+reCh. 6.2 - 31-50 Differentiate the function. f(x)=(3x25x)exCh. 6.2 - 31-50 Differentiate the function. y=ex1exCh. 6.2 - 31-50 Differentiate the function. y=eax3Ch. 6.2 - 31-50 Differentiate the function. g(x)=ex2xCh. 6.2 - 31-50 Differentiate the function. y=etanCh. 6.2 - 31-50 Differentiate the function. V(t)=4+ttetCh. 6.2 - 31-50 Differentiate the function. f(x)=x2exx2+exCh. 6.2 - 31-50 Differentiate the function. y=x2e1/xCh. 6.2 - 31-50 Differentiate the function. y=x2e3xCh. 6.2 - 31-50 Differentiate the function. f(t)=tan(1+e2t)Ch. 6.2 - 31-50 Differentiate the function. f(t)=eatsinbtCh. 6.2 - 31-50 Differentiate the function. f(z)=ez/(z1)Ch. 6.2 - 31-50 Differentiate the function. F(t)=etsin2tCh. 6.2 - 31-50 Differentiate the function....Ch. 6.2 - 31-50 Differentiate the function. g(u)=esecu2Ch. 6.2 - 31-50 Differentiate the function. y=1+xe2xCh. 6.2 - 31-50 Differentiate the function. y=cos(1e2x1+e2x)Ch. 6.2 - 31-50 Differentiate the function....Ch. 6.2 - 51-52 Find an equation of the tangent line to the...Ch. 6.2 - 51-52 Find an equation of the tangent line to the...Ch. 6.2 - Find yifex/y=xy.Ch. 6.2 - Find an equation of the tangent line to the curve...Ch. 6.2 - Show that the function y=ex+ex/2 satisfies the...Ch. 6.2 - Show that the function y=Aex+Bxex satisfies the...Ch. 6.2 - For what values of r does the function y=erx...Ch. 6.2 - Find the values of for which y=ex satisfies the...Ch. 6.2 - If f(x)=e2x, find a formula for f(n)(x).Ch. 6.2 - Find the thousandth derivative of f(x)=xex.Ch. 6.2 - a Use the Intermediate Value Theorem to show that...Ch. 6.2 - Use a graph to find an initial approximation to...Ch. 6.2 - Use the graph of V in Figure 11 to estimate the...Ch. 6.2 - A researcher is trying to determine the doubling...Ch. 6.2 - Under certain circumstances a rumor spreads...Ch. 6.2 - An object is attached to the end of a vibrating...Ch. 6.2 - Find the absolute maximum value of the function...Ch. 6.2 - Find the absolute minimum value of the function...Ch. 6.2 - 69-70 Find the absolute maximum and absolute...Ch. 6.2 - 69-70 Find the absolute maximum and absolute...Ch. 6.2 - 71-72 Find a the intervals of increase or...Ch. 6.2 - 71-72 Find a the intervals of increase or...Ch. 6.2 - 73-75 Discuss the curve using the guidelines of...Ch. 6.2 - 73-75 Discuss the curve using the guidelines of...Ch. 6.2 - 73-75 Discuss the curve using the guidelines of...Ch. 6.2 - Let g(x)=ecx+f(x) and h(x)=ekxf(x), where...Ch. 6.2 - A drug response curve describes the level of...Ch. 6.2 - After an antibiotic tablet is taken, the...Ch. 6.2 - After the consumption of an alcoholic beverage,...Ch. 6.2 - 80-81 Draw a graph of f that shows all the...Ch. 6.2 - 80-81 Draw a graph of f that shows all the...Ch. 6.2 - The family of bell-shaped curves y=12e(x)2/(22)...Ch. 6.2 - 83-94 Evaluate the integral. 01(xe+ex)dxCh. 6.2 - 83-94 Evaluate the integral. 55edxCh. 6.2 - 83-94 Evaluate the integral. 02dxexCh. 6.2 - 83-94 Evaluate the integral. x2ex3dxCh. 6.2 - 83-94 Evaluate the integral. ex1+exdxCh. 6.2 - 83-94 Evaluate the integral. (1+ex)2exdxCh. 6.2 - 83-94 Evaluate the integral. (ex+ex)2dxCh. 6.2 - 83-94 Evaluate the integral. ex(4+ex)5dxCh. 6.2 - 83-94 Evaluate the integral. eu(1eu)2duCh. 6.2 - 83-94 Evaluate the integral. esincosdCh. 6.2 - 83-94 Evaluate the integral. 12e1/xx2dxCh. 6.2 - 83-94 Evaluate the integral. 011+exexdxCh. 6.2 - Find, correct to three decimal places, the area of...Ch. 6.2 - Find f(x) if f(x)=3ex+5sinx,f(0)=1, and f(0)=2.Ch. 6.2 - Find the volume of the solid obtained by rotating...Ch. 6.2 - Find the volume of the solid obtained by rotating...Ch. 6.2 - The error function erf(x)=20xet2dt Is used in...Ch. 6.2 - Show that the function y=ex2erf(x) Satisfies the...Ch. 6.2 - An oil storage tank ruptures at time t=0 and oil...Ch. 6.2 - A bacteria population starts with 400 bacteria and...Ch. 6.2 - Dialysis treatment removes urea and other waste...Ch. 6.2 - The rate of growth of a fish population was...Ch. 6.2 - If f(x)=3+x+ex, find (f1)(4).Ch. 6.2 - Evaluate limxesinx1x.Ch. 6.2 - If you graph the function f(x)=1e1/x1+e1/x Youll...Ch. 6.2 - Graph several members of the family of functions...Ch. 6.2 - a Show that ex1+x if x0. Hint: Show that...Ch. 6.2 - a Use the inequality of Exercise 109a to show...Ch. 6.2 - a Use mathematical induction to prove that for x0...Ch. 6.3 - a How is logarithmic function y=logbx defined? b...Ch. 6.3 - a What is the natural logarithm? b What is the...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - Use the properties of logarithms to expand the...Ch. 6.3 - Use the properties of logarithms to expand the...Ch. 6.3 - Use the properties of logarithms to expand the...Ch. 6.3 - Use the properties of logarithms to expand the...Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - Use formula 7 to evaluate each logarithm correct...Ch. 6.3 - 20-22 Use formula 7 to graph the given functions...Ch. 6.3 - 20-22 Use formula 7 to graph the given functions...Ch. 6.3 - 20-22 Use formula 7 to graph the given functions...Ch. 6.3 - Make a rough sketch of the graph of each function....Ch. 6.3 - 23-24 Make a rough sketch of the graph of each...Ch. 6.3 - 25-26 a What are the domain and range of f? b What...Ch. 6.3 - 25-26 a What are the domain and range of f? b What...Ch. 6.3 - 27-36 Solve each equation for x a e74x=6 b...Ch. 6.3 - 27-36 Solve each equation for x a ln(x21)=3 b...Ch. 6.3 - 27-36 Solve each equation for x a 2x5=3 b...Ch. 6.3 - 27-36 Solve each equation for x a e3x+1=k b...Ch. 6.3 - 27-36 Solve each equation for x ee2x=1Ch. 6.3 - 27-36 Solve each equation for x 10(1+ex)1=3Ch. 6.3 - 27-36 Solve each equation for x ln(lnx)=1Ch. 6.3 - 27-36 Solve each equation for x eex=10Ch. 6.3 - 27-36 Solve each equation for x e2xex6=0Ch. 6.3 - 27-36 Solve each equation for x. ln(2x+1)=2lnxCh. 6.3 - 37-38 Find the solution of the equation correct to...Ch. 6.3 - 37-38 Find the solution of the equation correct to...Ch. 6.3 - 37-38 Find the solution of the equation correct to...Ch. 6.3 - 37-38 Find the solution of the equation correct to...Ch. 6.3 - Suppose that the graph of y=log2x is drawn on a...Ch. 6.3 - The velocity of a particle that moves in a...Ch. 6.3 - The geologist C. F. Richter defined the magnitude...Ch. 6.3 - A sound so faint that it can just be heard has...Ch. 6.3 - If a bacteria population starts with 100 bacteria...Ch. 6.3 - When a camera flash goes off, the batteries...Ch. 6.3 - 47-52 Find the limit. limx3+In(x29)Ch. 6.3 - 47-52 Find the limit. limx2log5(8xx4)Ch. 6.3 - Find the limit. limx0In(cosx)Ch. 6.3 - Find the limit. limx0+In(sinx)Ch. 6.3 - 47-52 Find the limit. limx[In(1+x2)In(1+x)]Ch. 6.3 - 47-52 Find the limit. limx[In(2+x)In(1+x)]Ch. 6.3 - 53-54 Find the domain of the function....Ch. 6.3 - 53-54 Find the domain of the function....Ch. 6.3 - 55-57 Find a the domain of f and b f1 and its...Ch. 6.3 - 55-57 Find a the domain of f and b f1 and its...Ch. 6.3 - 55-57 Find a the domain of f and b f1 and its...Ch. 6.3 - a What are the values of eIn300 and In(e300)? b...Ch. 6.3 - 59-64 Find the inverse function. y=2In(x1)Ch. 6.3 - 59-64 Find the inverse function. g(x)=log4(x3+2)Ch. 6.3 - 59-64 Find the inverse function. f(x)=ex3Ch. 6.3 - 59-64 Find the inverse function. y=(Inx2),x1Ch. 6.3 - 59-64 Find the inverse function. y=32x4Ch. 6.3 - 59-64 Find the inverse function. y=1ex1+exCh. 6.3 - On what interval is the function f(x)=e3xex...Ch. 6.3 - On what interval is the curve y=2exe3x concave...Ch. 6.3 - a Show that the function f(x)=In(x+x2+1) is an odd...Ch. 6.3 - Find an equation of the tangent to the curve y=ex...Ch. 6.3 - Show that the equation x1/Inx=2 has no solution....Ch. 6.3 - Any function of the form f(x)=[g(x)]h(x), where...Ch. 6.3 - Let b1. Prove, using definitions 3.4.6 and 3.4.7,...Ch. 6.3 - a Compare the rates of growth of f(x)=x0.1 and...Ch. 6.3 - Solve the inequality In(x22x2)0.Ch. 6.3 - A prime number is a positive integer that has no...Ch. 6.4 - Explain why the natural logarithmic function y=lnx...Ch. 6.4 - 2-26 Differentiate the function. f(x)=xlnxxCh. 6.4 - 2-26 Differentiate the function. f(x)=sin(lnx)Ch. 6.4 - 2-26 Differentiate the function. f(x)=ln(sin2x)Ch. 6.4 - 2-26 Differentiate the function. f(x)=ln1xCh. 6.4 - 2-26 Differentiate the function. y=1lnxCh. 6.4 - 2-26 Differentiate the function....Ch. 6.4 - 2-26 Differentiate the function. f(x)=log10xCh. 6.4 - 2-26 Differentiate the function. g(x)=ln(xe2x)Ch. 6.4 - 2-26 Differentiate the function. g(t)=1+lntCh. 6.4 - 2-26 Differentiate the function. F(t)=(lnt2)sintCh. 6.4 - 2-26 Differentiate the function. h(x)=ln(x+x21)Ch. 6.4 - 2-26 Differentiate the function....Ch. 6.4 - 2-26 Differentiate the function. P(v)=lnv1vCh. 6.4 - 2-26 Differentiate the function. f(u)=lnu1+ln(2u)Ch. 6.4 - 2-26 Differentiate the function. y=ln|1+tt3|Ch. 6.4 - 2-26 Differentiate the function. f(x)=x5+5xCh. 6.4 - 2-26 Differentiate the function. g(x)=xsin(2x)Ch. 6.4 - 2-26 Differentiate the function. T(z)=2zlog2zCh. 6.4 - 2-26 Differentiate the function. y=ln(cscxcotx)Ch. 6.4 - 2-26 Differentiate the function. y=ln(ex+xex)Ch. 6.4 - 2-26 Differentiate the function. H(z)=lna2z2a2+z2Ch. 6.4 - 2-26 Differentiate the function. y=tan[ln(ax+b)]Ch. 6.4 - 2-26 Differentiate the function. y=log2(xlog5x)Ch. 6.4 - 2-26 Differentiate the function. G(x)=4C/xCh. 6.4 - 2-26 Differentiate the function. F(t)=3cos2tCh. 6.4 - 27-30 Find y and y. y=xlnxCh. 6.4 - 27-30 Find y and y. y=lnx1+lnxCh. 6.4 - 27-30 Find y and y. y=ln|secx|Ch. 6.4 - 27-30 Find y and y. y=ln(1+lnx)Ch. 6.4 - 31-34 Differentiate f and find the domain of f....Ch. 6.4 - 31-34 Differentiate f and find the domain of f....Ch. 6.4 - 31-34 Differentiate f and find the domain of f....Ch. 6.4 - 31-34 Differentiate f and find the domain of f....Ch. 6.4 - If f(x)=ln(x+lnx), find f(1)Ch. 6.4 - If f(x)=cos(lnx2), find f(1).Ch. 6.4 - 37-38 Find an equation of the tangent line to the...Ch. 6.4 - 37-38 Find an equation of the tangent line to the...Ch. 6.4 - If f(x)=sinx+lnx, find f(x). Check that your...Ch. 6.4 - Find equations of the tangent lines to the curve...Ch. 6.4 - Let f(x)=cx+ln(cosx). For what value of c is...Ch. 6.4 - Let f(x)=logb(3x2). For what value of b is f(1)=3?Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - Find y if y=ln(x2+y2).Ch. 6.4 - Find y if xy=yx.Ch. 6.4 - Find a formula for f(n)(x) if f(x)=ln(x1).Ch. 6.4 - Find d9dx9(x8lnx).Ch. 6.4 - 59-60 Use a graph to estimate the roots of the...Ch. 6.4 - 59-60 Use a graph to estimate the roots of the...Ch. 6.4 - Find the intervals of concavity and the inflection...Ch. 6.4 - Find the absolute minimum value of the function...Ch. 6.4 - 63-66 Discuss the curve under the guidelines of...Ch. 6.4 - 63-66 Discuss the curve under the guidelines of...Ch. 6.4 - 63-66 Discuss the curve under the guidelines of...Ch. 6.4 - 63-66 Discuss the curve under the guidelines of...Ch. 6.4 - If f(x)=ln(2x+xsinx), use the graphs of f,f and f...Ch. 6.4 - Investigate the family of curves f(x)=ln(x2+c)....Ch. 6.4 - The flash unit on a camera operates by storing...Ch. 6.4 - The table gives the US population from 1790 to...Ch. 6.4 - 71-82 Evaluate the integral. 243xdxCh. 6.4 - 71-82 Evaluate the integral. 03dx5x+1Ch. 6.4 - 71-82 Evaluate the integral. 12dt83tCh. 6.4 - 71-82 Evaluate the integral. 49(x+1x)2dxCh. 6.4 - 71-82 Evaluate the integral. 1ex2+x+1xdxCh. 6.4 - 71-82 Evaluate the integral. cos(lnt)tdtCh. 6.4 - 71-82 Evaluate the integral. (lnx)22dxCh. 6.4 - 71-82 Evaluate the integral. cosx2+sinxdxCh. 6.4 - 71-82 Evaluate the integral. sin2x1+cos2xdxCh. 6.4 - 71-82 Evaluate the integral. exex+1dxCh. 6.4 - 71-82 Evaluate the integral. 042sdsCh. 6.4 - 71-82 Evaluate the integral. x2x2dxCh. 6.4 - Show that cotxdx=ln|sinx|+C by a differentiating...Ch. 6.4 - Sketch the region enclosed by the curves y=lnxx...Ch. 6.4 - Find the volume of the solid obtained by rotating...Ch. 6.4 - Find the volume of the solid obtained by rotating...Ch. 6.4 - The work done by a gas when it expands from volume...Ch. 6.4 - Find f if f(x)=x2,x0,f(1)=0, and f(2)=0.Ch. 6.4 - If g is the inverse function of f(x)=2x+lnx, find...Ch. 6.4 - If f(x)=ex+lnx and h(x)=f1(x), find h(e).Ch. 6.4 - For what values of m do the line y=mx and the...Ch. 6.4 - a Find the linear approximation to f(x)=lnx near...Ch. 6.4 - Use the definition of derivative to prove that...Ch. 6.4 - Show that limn(1+xn)n=ex for any x0.Ch. 6.2Star - 1-4 Use the Laws of Logarithms to expand the...Ch. 6.2Star - 1-4 Use the Laws of Logarithms to expand the...Ch. 6.2Star - 1-4 Use the Laws of Logarithms to expand the...Ch. 6.2Star - Use the Laws of Logarithms to expand the quantity....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 11-14 Make a rough sketch of the graph of each...Ch. 6.2Star - 11-14 Make a rough sketch of the graph of each...Ch. 6.2Star - 11-14 Make a rough sketch of the graph of each...Ch. 6.2Star - 11-14 Make a rough sketch of the graph of each...Ch. 6.2Star - 15-16 Find the limit. limx3+ln(x29)Ch. 6.2Star - 15-16 Find the limit. limx[ln(2+x)ln(1+x)]Ch. 6.2Star - 17-36 Differentiate the function. f(x)=x3lnxCh. 6.2Star - 17-36 Differentiate the function. f(x)=xlnxxCh. 6.2Star - 17-36 Differentiate the function. f(x)=sin(lnx)Ch. 6.2Star - 17-36 Differentiate the function. f(x)=ln(sin2x)Ch. 6.2Star - 17-36 Differentiate the function. f(x)=ln1xCh. 6.2Star - 17-36 Differentiate the function. y=1lnxCh. 6.2Star - 17-36 Differentiate the function. f(x)=sinxln(5x)Ch. 6.2Star - Differentiate the function. h(x)=ln(x+x21)Ch. 6.2Star - 17-36 Differentiate the function. g(x)=lnaxa+xCh. 6.2Star - Differentiate the function. g(t)=1+lntCh. 6.2Star - 17-36 Differentiate the function....Ch. 6.2Star - Differentiate the function. H(z)=lna2z2a2+z2Ch. 6.2Star - 17-36 Differentiate the function. F(t)=(lnt)2sintCh. 6.2Star - 17-36 Differentiate the function. P(v)=lnv1vCh. 6.2Star - 17-36 Differentiate the function. f(u)=lnu1+ln(2u)Ch. 6.2Star - 17-36 Differentiate the function. y=(lntanx)2Ch. 6.2Star - 17-36 Differentiate the function. y=ln|2x5x2|Ch. 6.2Star - 17-36 Differentiate the function. y=lntan2xCh. 6.2Star - 17-36 Differentiate the function. y=tan[ln(ax+b)]Ch. 6.2Star - 17-36 Differentiate the function. y=ln(cscxcotx)Ch. 6.2Star - Find y and y. y=xlnxCh. 6.2Star - 37-38 Find y and y. y=ln(1+lnx)Ch. 6.2Star - 39-42 Differentiate f and find the domain of f....Ch. 6.2Star - 39-42 Differentiate f and the domain of f....Ch. 6.2Star - Differentiate f and the domain of f. f(x)=iInxCh. 6.2Star - 39-42 Differentiate f and the domain of f....Ch. 6.2Star - If f(x)=In(x+Inx), find f(1).Ch. 6.2Star - If f(x)=Inxx, find f"(e).Ch. 6.2Star - 45-46 Find f(x).Check that your answer is...Ch. 6.2Star - 45-46 Find f(x).Check that your answer is...Ch. 6.2Star - 47-48 Find an equation of tangent line to the...Ch. 6.2Star - 47-48 Find an equation of tangent line to the...Ch. 6.2Star - Find y if y=In(x2+y2)Ch. 6.2Star - Find y if Inx=ysinxCh. 6.2Star - Find a formula for f(n)(x) if f(x)=In(x1)Ch. 6.2Star - Find d9dx9(x8Inx).Ch. 6.2Star - 53-54 Use a graph to estimate the roots of the...Ch. 6.2Star - 53-54 Use a graph to estimate the roots of the...Ch. 6.2Star - 55-58 Discuss the curve under the guidelines of...Ch. 6.2Star - 55-58 Discuss the curve under the guidelines of...Ch. 6.2Star - 55-58 Discuss the curve under the guidelines of...Ch. 6.2Star - 55-58 Discuss the curve under the guidelines of...Ch. 6.2Star - If f(x)=In(2x+xsinx), use the graphs of f,f, and...Ch. 6.2Star - Investigate the family of curves f(x)=In(x2+c)....Ch. 6.2Star - 61-64 Use logarithmic differentiation to find the...Ch. 6.2Star - 61-64 Use logarithmic differentiation to find the...Ch. 6.2Star - 61-64 Use logarithmic differentiation to find the...Ch. 6.2Star - 61-64 Use logarithmic differentiation to find the...Ch. 6.2Star - 65-74 Evaluate the integral. 243xdxCh. 6.2Star - 65-74 Evaluate the integral. 03dx5x+1Ch. 6.2Star - 65-74 Evaluate the integral. 12dt83tCh. 6.2Star - Evaluate the integral. 49(x+1x)2dxCh. 6.2Star - 65-74 Evaluate the integral. 1ex2+x+1xdxCh. 6.2Star - 65-74 Evaluate the integral. e6dxxsinxCh. 6.2Star - 65-74 Evaluate the integral. (Inx)2xdxCh. 6.2Star - 65-74 Evaluate the integral. cosx2+sinxdxCh. 6.2Star - 65-74 Evaluate the integral. sin2x1+cos2xdxCh. 6.2Star - 65-74 Evaluate the integral. cos(Int)tCh. 6.2Star - Show that cotxdx=In|sinx|+C by a differentiating...Ch. 6.2Star - Sketch the region enclosed by the curves y=Inxx...Ch. 6.2Star - Find the volume of the solid obtained by rotating...Ch. 6.2Star - Find the volume of the solid obtained by rotating...Ch. 6.2Star - The work done by a gas when it expands from volume...Ch. 6.2Star - Find f if f(x)=x2, x0, f(1)=0, and f(2)=0.Ch. 6.2Star - If g is the inverse function of f(x)=2x+Inx, find...Ch. 6.2Star - a Find the linear approximation to f(x)=Inx near...Ch. 6.2Star - a By comparing areas, show that 131.5512 b Use the...Ch. 6.2Star - a Find an equation of the tangent line to the...Ch. 6.2Star - By comparing areas, show that...Ch. 6.2Star - Prove the third law of logarithms. Hint: Start by...Ch. 6.2Star - For what values of m do the line y=mx and the...Ch. 6.2Star - a Compare the rates of growth of f(x)=x0.1 and...Ch. 6.2Star - Use the definition of derivative to prove that...Ch. 6.3Star - Sketch, by hand, the graph of the function f(x)=ex...Ch. 6.3Star - 2-4 Simplify each expression. a eIn15b In(1/e2)Ch. 6.3Star - Simplify each expression. a eIn2b eIn(Ine3)Ch. 6.3Star - 2-4 Simplify each expression. a Inesinxb ex+InxCh. 6.3Star - Solve each equation for x. a e74x=6b In(3x10)=2Ch. 6.3Star - 5-12 Solve each equation for x. ln(x21)=3Ch. 6.3Star - Solve each equation for x. a e3x+1=kb...Ch. 6.3Star - Solve each equation for x. a ln(lnx)=1b eex=10Ch. 6.3Star - 5-12 Solve each equation for x. ee2x=1Ch. 6.3Star - 5-12 Solve each equation for x. 10(1+ex)1=3Ch. 6.3Star - 5-12 Solve each equation for x. e2xex6=0Ch. 6.3Star - 5-12 Solve each equation for x. ln(2x+1)=2lnxCh. 6.3Star - Find the solution of the equation correct to four...Ch. 6.3Star - Find the solution of the equation correct to four...Ch. 6.3Star - Solve each inequality for x. a lnx0b ex5Ch. 6.3Star - Solve each inequality for x. a 1e3x12b 12lnx3Ch. 6.3Star - 17-20 Make a rough sketch of the graph of the...Ch. 6.3Star - 17-20 Make a rough sketch of the graph of the...Ch. 6.3Star - 17-20 Make a rough sketch of the graph of the...Ch. 6.3Star - 17-20 Make a rough sketch of the graph of the...Ch. 6.3Star - 21-22 Find a the domain of f and b f1 and its...Ch. 6.3Star - 21-22 Find a the domain of f and b f1 and its...Ch. 6.3Star - 23-26: Find the inverse function y=2ln(x1)Ch. 6.3Star - 23-26: Find the inverse function y=(lnx)2,x1Ch. 6.3Star - 23-26: Find the inverse function f(x)=ex3Ch. 6.3Star - 23-26: Find the inverse function y=1ex1+exCh. 6.3Star - 27-32 Find the limit. limxe3xe3xe3x+e3xCh. 6.3Star - 27-32 Find the limit. limxex2Ch. 6.3Star - 27-32 Find the limit. limx2+e3/(2x)Ch. 6.3Star - 27-32 Find the limit. limx2e3/(2x)Ch. 6.3Star - 27-32 Find the limit. limx(e2xcosx)Ch. 6.3Star - 27-32 Find the limit. limx(/2)+etanxCh. 6.3Star - 33-52 Differentiate the function. f(x)=e5Ch. 6.3Star - 33-52 Differentiate the function. k(r)=er+reCh. 6.3Star - 33-52 Differentiate the function. f(x)=(3x25x)exCh. 6.3Star - 33-52 Differentiate the function. y=ex1exCh. 6.3Star - 33-52 Differentiate the function. y=eax3Ch. 6.3Star - 33-52 Differentiate the function. g(x)=ex2xCh. 6.3Star - 33-52 Differentiate the function. y=etanCh. 6.3Star - 33-52 Differentiate the function. V(t)=4+ttetCh. 6.3Star - 33-52 Differentiate the function. f(x)=x2exx2+exCh. 6.3Star - 33-52 Differentiate the function. y=x2e1/xCh. 6.3Star - 33-52 Differentiate the function. y=x2e3xCh. 6.3Star - 33-52 Differentiate the function. f(t)=tan(1+e2t)Ch. 6.3Star - 33-52 Differentiate the function. f(t)=eatsinbtCh. 6.3Star - 33-52 Differentiate the function. f(z)=ez/(z1)Ch. 6.3Star - 33-52 Differentiate the function. F(t)=etsin2tCh. 6.3Star - 33-52 Differentiate the function....Ch. 6.3Star - 33-52 Differentiate the function. g(u)=esecu2Ch. 6.3Star - 33-52 Differentiate the function. y=1+xe2xCh. 6.3Star - 33-52 Differentiate the function. y=cos(1e2x1+e2x)Ch. 6.3Star - 33-52 Differentiate the function....Ch. 6.3Star - 53-54 Find an equation of the tangent line to the...Ch. 6.3Star - 53-54 Find an equation of the tangent line to the...Ch. 6.3Star - Find y if ex/y=xyCh. 6.3Star - Find an equation of the tangent line to the curve...Ch. 6.3Star - Show that the function y=ex+ex/2 satisfies the...Ch. 6.3Star - Show that the function y=Aex+Bxex satisfies the...Ch. 6.3Star - For what values of r does the function y=erx...Ch. 6.3Star - Find the values of for which y=ex satisfies the...Ch. 6.3Star - If f(x)=e2x, find a formula for f(n)(x).Ch. 6.3Star - Find the thousandth derivative of f(x)=xex.Ch. 6.3Star - a Use the Intermediate Value theorem to show that...Ch. 6.3Star - Use a graph to find an initial approximation to...Ch. 6.3Star - Under certain circumstances a rumor spreads...Ch. 6.3Star - An object is attached to the end of a vibrating...Ch. 6.3Star - Find the absolute maximum value of the function...Ch. 6.3Star - Find the absolute minimum value of the function...Ch. 6.3Star - 69-70 Find the absolute maximum and absolute...Ch. 6.3Star - 69-70 Find the absolute maximum and absolute...Ch. 6.3Star - 71-72 Find a the intervals of increase or...Ch. 6.3Star - 71-72 Find a the intervals of increase or...Ch. 6.3Star - 73-75 Discuss the curve using the guidelines of...Ch. 6.3Star - 73-75 Discuss the curve using the guidelines of...Ch. 6.3Star - 73-75 Discuss the curve using the guidelines of...Ch. 6.3Star - Let g(x)=ecx+f(x) and h(x)=ekxf(x), where f(0)=3,...Ch. 6.3Star - A drug response curve describes the level of...Ch. 6.3Star - After an antibiotic tablet is taken, the...Ch. 6.3Star - After the consumption of an alcoholic beverage,...Ch. 6.3Star - 80-81. Draw a graph of f that shows all the...Ch. 6.3Star - 80-81. Draw a graph of f that shows all the...Ch. 6.3Star - The family of bell-shaped curves y=12e(x)2/(22)...Ch. 6.3Star - 83-94 Evaluate the integral. 01(xe+ex)dxCh. 6.3Star - 83-94 Evaluate the integral. 55edxCh. 6.3Star - 83-94 Evaluate the integral. 02dxexCh. 6.3Star - 83-94 Evaluate the integral. x2ex3dxCh. 6.3Star - 83-94 Evaluate the integral. ex1+exdxCh. 6.3Star - 83-94 Evaluate the integral. (1+ex)2exdxCh. 6.3Star - 83-94 Evaluate the integral. (ex+ex)2dxCh. 6.3Star - 83-94 Evaluate the integral. ex(4+ex)5dxCh. 6.3Star - 83-94 Evaluate the integral. eu(1eu)2duCh. 6.3Star - 83-94 Evaluate the integral. esincosdCh. 6.3Star - 83-94 Evaluate the integral. 12e1/xx2dxCh. 6.3Star - 83-94 Evaluate the integral. 011+exexdxCh. 6.3Star - Find, correct to three decimal places, the area of...Ch. 6.3Star - Find f(x) if f(x)=3ex+5sinx,f(0)=1, and f(0)=2.Ch. 6.3Star - Find the volume of the solid obtained by rotating...Ch. 6.3Star - Find the volume of the solid obtained by rotating...Ch. 6.3Star - The error function erf(x)=20xet2dt is used in...Ch. 6.3Star - Show that the function y=ex2erf(x) satisfies the...Ch. 6.3Star - An oil storage tank ruptures at time t = 0 and oil...Ch. 6.3Star - A bacteria population starts with 400 bacteria and...Ch. 6.3Star - Dialysis treatment removes urea and other waste...Ch. 6.3Star - The rate of growth of a fish population was...Ch. 6.3Star - If you graph the function f(x)=1e1/x1+e1/x youll...Ch. 6.3Star - Graph several members of the family of functions...Ch. 6.3Star - Prove the second law of exponents see 7.Ch. 6.3Star - Prove the third law of exponents see 7.Ch. 6.3Star - a Show that ex1+xifx0. Hint: Show that...Ch. 6.3Star - a Use the inequality of Exercise 109a to show...Ch. 6.3Star - a Use mathematical induction to prove that for x0...Ch. 6.3Star - This exercise illustrates Exercise 111c for the...Ch. 6.4Star - a Write an equation that defines bx when b is a...Ch. 6.4Star - a If b is a positive number and b1, how is logbx...Ch. 6.4Star - 3-6 Write the expression as a power of e. 4Ch. 6.4Star - 3-6 Write the expression as a power of e. x5Ch. 6.4Star - 3-6 Write the expression as a power of e. 10x2Ch. 6.4Star - 3-6 Write the expression as a power of e....Ch. 6.4Star - 7-10 Evaluate the expression. a log232 b log82Ch. 6.4Star - 7-10 Evaluate the expression. a log1010 b...Ch. 6.4Star - 7-10 Evaluate the expression. a log1040+log102.5 b...Ch. 6.4Star - 7-10 Evaluate the expression. a loga1a b...Ch. 6.4Star - 11-12 Graph the given functions on a common...Ch. 6.4Star - 11-12 Graph the given functions on a common...Ch. 6.4Star - Use Formula 6 to evaluate each logarithm correct...Ch. 6.4Star - 14-16 Use Formula 6 to graph the given functions...Ch. 6.4Star - 14-16 Use Formula 6 to graph the given functions...Ch. 6.4Star - 14-16 Use Formula 6 to graph the given functions...Ch. 6.4Star - 17-18 Find the exponential function f(x)=Cbx whose...Ch. 6.4Star - 17-18 Find the exponential function f(x)=Cbx whose...Ch. 6.4Star - a Suppose the graphs of f(x)=x2 and g(x)=2xare...Ch. 6.4Star - Compare the rates of growth of the functions...Ch. 6.4Star - 21-24 Find the limit. limx(1.001)xCh. 6.4Star - 21-24 Find the limit. limx(1.001)xCh. 6.4Star - 21-24 Find the limit. limt2t2Ch. 6.4Star - 21-24 Find the limit. limx3+log10(x25x+6)Ch. 6.4Star - 25-42 Differentiate the function. f(x)=x5+5xCh. 6.4Star - 25-42 Differentiate the function. g(x)=xsin(2x)Ch. 6.4Star - 25-42 Differentiate the function. G(x)=4c/xCh. 6.4Star - 25-42 Differentiate the function. F(t)=3cos2tCh. 6.4Star - 25-42 Differentiate the function. L(v)=tan(4v2)Ch. 6.4Star - 25-42 Differentiate the function. G(u)=(1+10lnu)6Ch. 6.4Star - 25-42 Differentiate the function. f(x)=log2(13x)Ch. 6.4Star - 25-42 Differentiate the function. f(x)=log10xCh. 6.4Star - 25-42 Differentiate the function. y=xlog4sinxCh. 6.4Star - 25-42 Differentiate the function. y=log2(xlog5x)Ch. 6.4Star - 25-42 Differentiate the function. y=xxCh. 6.4Star - 25-42 Differentiate the function. y=xcosxCh. 6.4Star - 25-42 Differentiate the function. y=xsinxCh. 6.4Star - 25-42 Differentiate the function. y=(x)xCh. 6.4Star - 25-42 Differentiate the function. y=(cosx)xCh. 6.4Star - 25-42 Differentiate the function. y=(sinx)lnxCh. 6.4Star - 25-42 Differentiate the function. y=(tanx)1/xCh. 6.4Star - 25-42 Differentiate the function. y=(lnx)cosxCh. 6.4Star - Find an equation of the tangent line to the curve...Ch. 6.4Star - If f(x)=xcosx, find f(x). Check that your answer...Ch. 6.4Star - 45-50 Evaluate the integral. 042sdsCh. 6.4Star - 45-50 Evaluate the integral. (x5+5x)dxCh. 6.4Star - 45-50 Evaluate the integral. log10xxdxCh. 6.4Star - 45-50 Evaluate the integral. x2x2dxCh. 6.4Star - 45-50 Evaluate the integral. 3sincosdCh. 6.4Star - 45-50 Evaluate the integral. 2x2x+1dxCh. 6.4Star - Find the area of the region bounded by the curves...Ch. 6.4Star - The region under the curve y=10x from x=0 to x=1...Ch. 6.4Star - Use a graph to find the root of the equation...Ch. 6.4Star - Find y if xy=yx.Ch. 6.4Star - Find the inverse function of g(x)=log4(x3+2).Ch. 6.4Star - Calculate limx0+xlnxCh. 6.4Star - The geologist C. F. Richter defined the magnitude...Ch. 6.4Star - A sound so faint that it can just be heard has...Ch. 6.4Star - Referring to Exercise 58, find the rate of change...Ch. 6.4Star - According to the Beer-Lambert Law, the light...Ch. 6.4Star - After the consumption of an alcoholic beverage,...Ch. 6.4Star - In this section we modeled the world population...Ch. 6.4Star - Use the graph of V in Figure 9 to estimate the...Ch. 6.4Star - A researcher is trying to determine the doubling...Ch. 6.4Star - The flash unit on a camera operates by storing...Ch. 6.4Star - The table gives the US population from 1790 to...Ch. 6.4Star - Prove the second law of exponents see 3.Ch. 6.4Star - Prove the fourth law of exponents see 3.Ch. 6.4Star - Deduce the following laws of logarithms from 3: a...Ch. 6.4Star - Show that limn(1+xn)n=ex for any x0.Ch. 6.5 - A population of protozoa develops with a constant...Ch. 6.5 - A common inhabitant of human intestines is the...Ch. 6.5 - A bacteria culture initially contains 100 cells...Ch. 6.5 - A bacteria culture grows with constant relative...Ch. 6.5 - The table gives estimates of the world population,...Ch. 6.5 - The table gives the population of Indonesia, in...Ch. 6.5 - Experiments show that if the chemical reaction...Ch. 6.5 - Strontium-90 has a half-life of 28 days. a A...Ch. 6.5 - The half-life of cesium-137 is 30 years. Suppose...Ch. 6.5 - A sample of tritium-3 decayed to 94.5 of its...Ch. 6.5 - Scientists can determine the age of ancient...Ch. 6.5 - Dinosaur fossils are too old to be reliably dated...Ch. 6.5 - Dinosaur fossils are often dated by using an...Ch. 6.5 - A curve passes through the point (0,5) and has the...Ch. 6.5 - A roast turkey is taken from an oven when its...Ch. 6.5 - In a murder investigation, the temperature of the...Ch. 6.5 - When a cold drink is taken from a refrigerator,...Ch. 6.5 - A freshly brewed cup of coffee has temperature 95C...Ch. 6.5 - The rate of change of atmospheric pressure P with...Ch. 6.5 - a If 1000 is borrowed at 8 interest, find the...Ch. 6.5 - a If 3000 is invested at 5 interest, find the...Ch. 6.5 - a How long will it take an investment to double in...Ch. 6.6 - Find the exact value of each expression. a...Ch. 6.6 - Find the exact value of each expression. a tan13 b...Ch. 6.6 - Find the exact value of each expression. a csc12 b...Ch. 6.6 - Find the exact value of each expression. a cot1(3)...Ch. 6.6 - Find the exact value of each expression. a...Ch. 6.6 - Find the exact value of each expression. a...Ch. 6.6 - Find the exact value of each expression....Ch. 6.6 - Find the exact value of each expression....Ch. 6.6 - Find the exact value of each expression....Ch. 6.6 - Find the exact value of each expression....Ch. 6.6 - Prove that cos(sin1x)=1x2Ch. 6.6 - 12-14 Simplify the each expression. tan(sin1(x))Ch. 6.6 - 12-14 Simplify the each expression. sin(tan1(x))Ch. 6.6 - 12-14 Simplify the each expression. sin(2arccosx)Ch. 6.6 - 15-16 Graph the given functions on the same...Ch. 6.6 - 15-16 Graph the given functions on the same...Ch. 6.6 - Prove Formula 6 for the derivatives of cos1 by the...Ch. 6.6 - a Prove that sin1x+cos1x=/2 b Use part a to prove...Ch. 6.6 - Prove that ddt(cot1x)=11+x2.Ch. 6.6 - Prove that ddt(sec1x)=1xx21Ch. 6.6 - Prove that ddt(csc1x)=1xx21Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - 36-37 Find the derivative of the function. Find...Ch. 6.6 - 36-37 Find the derivative of the function. Find...Ch. 6.6 - Find y if tan1(x2y)=x+xy2.Ch. 6.6 - If g(x)=xsin1(x/4)+16x2, find g(2).Ch. 6.6 - Find an equation of the tangent line to the curve...Ch. 6.6 - Find f(x). Check that your answer is reasonable by...Ch. 6.6 - 41-42 Find f(x). Check that your answer is...Ch. 6.6 - 43-46 Find the limit. limx1+sin1xCh. 6.6 - 43-46 Find the limit. limx(1+x21+2x2)Ch. 6.6 - 43-46 Find the limit. limxarctan(ex)Ch. 6.6 - 43-46 Find the limit. limx0+tan1(Inx)Ch. 6.6 - Where should the point P be chosen on the line...Ch. 6.6 - A painting in an art gallery has height h and is...Ch. 6.6 - A ladder 10 ft long leans against a vertical wall....Ch. 6.6 - A lighthouse is located on a small island, 3 km...Ch. 6.6 - 51-54 Sketch the curve using the guidelines of...Ch. 6.6 - 51-54 Sketch the curve using the guidelines of...Ch. 6.6 - 51-54 Sketch the curve using the guidelines of...Ch. 6.6 - 51-54 Sketch the curve using the guidelines of...Ch. 6.6 - If f(x)=arctan(cos(3arcsinx)), use the graphs of...Ch. 6.6 - Investigate the family of curves given by...Ch. 6.6 - Find the most general antiderivative of the...Ch. 6.6 - Find g(t) if g(t)=2/1t2 and g(1)=5.Ch. 6.6 - Evaluate the integral. 1/3381+x2dxCh. 6.6 - Evaluate the integral. 1/21/261p2dpCh. 6.6 - Evaluate the integral. 01/2sin1x1x2dxCh. 6.6 - Evaluate the integral. 03/4dx1+16x2Ch. 6.6 - Evaluate the integral. 1+x1+x2dxCh. 6.6 - Evaluate the integral. 0/2sinx1+cos2xdxCh. 6.6 - Evaluate the integral. dx1x2sin1xCh. 6.6 - Evaluate the integral. 1xx24dxCh. 6.6 - Evaluate the integral. t21t6dtCh. 6.6 - Evaluate the integral. e2x1e4xdxCh. 6.6 - Evaluate the integral. dxx(1+x)Ch. 6.6 - Evaluate the integral. x1+x4dxCh. 6.6 - Use the method of Example 8 to show that, if a0,...Ch. 6.6 - The region under the curve y=1/x2+4 from x=0 to...Ch. 6.6 - Evaluate 01sin1xdx interpreting it as an area and...Ch. 6.6 - Prove that, for xy1,arctanx+arctany=arctanx+y1xy...Ch. 6.6 - Use the result of Exercise 74 to prove the...Ch. 6.6 - a Sketch the graph of the function...Ch. 6.6 - Use the method of Example 6 to prove the identity...Ch. 6.6 - Prove the identity arcsinx1x+1=2arctanx2Ch. 6.6 - Some authors define y=sec1xsecy=x and...Ch. 6.6 - Let f(x)=x arctan (1/x) if x0 and f(0)=0. a Is f...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 7-19 Prove the following identity sinh(x)=sinhx...Ch. 6.7 - 7-19 Prove the following identity cosh(x)=coshx...Ch. 6.7 - 7-19 Prove the following identity coshx+sinhx=exCh. 6.7 - 7-19 Prove the following identity coshxsinhx=exCh. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - 7-19 Prove the following identity coth2x1=csch2xCh. 6.7 - 7-19 Prove the identity...Ch. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - Prove the following identity cosh2x=coh2x+sinh2xCh. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - If tanhx=1213, find the values of the other...Ch. 6.7 - If coshx=53 and x0, find the values of the other...Ch. 6.7 - a Use the graphs of sinh, cosh, and tanh in...Ch. 6.7 - Use the definitions of the hyperbolic functions to...Ch. 6.7 - Prove the formulas given in Table 1 for the...Ch. 6.7 - Give an alternative solution to Example 3 by...Ch. 6.7 - Prove Equation 4.Ch. 6.7 - Prove Equation 5 using a the method of Example 3...Ch. 6.7 - For each of the following functions i give a...Ch. 6.7 - Prove the formulas given in Table 6 for the...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - Show that ddx1+tanhx1tanhx4=12ex/2Ch. 6.7 - Show that ddxarctan(tanhx)=sech2xCh. 6.7 - The Gateway Arch in St. Louis was designed by Eero...Ch. 6.7 - If a water wave with length L moves with velocity...Ch. 6.7 - A flexible cable always hangs in the shape of a...Ch. 6.7 - A telephone line hangs between two poles 14 m...Ch. 6.7 - Using principles from physics it can be shown that...Ch. 6.7 - A cable with linear density =2kg/m is strung from...Ch. 6.7 - A model for the velocity of a falling object after...Ch. 6.7 - a Show that any function of the form...Ch. 6.7 - If x=ln(sec+tan), show that sec=coshx.Ch. 6.7 - At what point of the curve y=coshx does the...Ch. 6.7 - Investigate the family of functions...Ch. 6.7 - 59-67 Evaluate the integral. sinhxcosh2xdxCh. 6.7 - 59-67 Evaluate the integral. sinh(1+4x)dxCh. 6.7 - 59-67 Evaluate the integral. sinhxxdxCh. 6.7 - 59-67 Evaluate the integral. tanhxdxCh. 6.7 - 59-67 Evaluate the integral. coshxcosh2x1dxCh. 6.7 - 59-67 Evaluate the integral. sech2x2+tanhxdxCh. 6.7 - 59-67 Evaluate the integral. 461t29dtCh. 6.7 - 59-67 Evaluate the integral. 01116t2+1dtCh. 6.7 - 59-67 Evaluate the integral. ex1e2xdxCh. 6.7 - Estimate the value of the number c such that the...Ch. 6.7 - a Use Newtons method or a graphing device to find...Ch. 6.7 - Show that the area of the shaded hyperbolic sector...Ch. 6.7 - Show that if a0 and b0, then there exist numbers ...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - 5-6 Use the graphs of f and g and their tangent...Ch. 6.8 - 5-6 Use the graphs of f and g and their tangent...Ch. 6.8 - The graph of a function f and its tangent line at...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 69-70 Use a graph to estimate the value of the...Ch. 6.8 - 69-70 Use a graph to estimate the value of the...Ch. 6.8 - 71-72 Illustrate IHospitals Rule by graphing both...Ch. 6.8 - 71-72 Illustrate IHospitals Rule by graphing both...Ch. 6.8 - Prove that limxexxn= for any positive integer n....Ch. 6.8 - Prove that limxlnxxp=0 for any number p0. This...Ch. 6.8 - 75-76 What happens if you try to use IHospitals...Ch. 6.8 - 75-76 What happens if you try to use IHospitals...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 83-85 a Graph the function. b Use lHospitals Rule...Ch. 6.8 - 83-85 a Graph the function. b Use lHospitals Rule...Ch. 6.8 - 83-85 a Graph the function. b Use lHospitals Rule...Ch. 6.8 - Investigate the family of curves given by...Ch. 6.8 - Investigate the family of curves f(x)=excx. In...Ch. 6.8 - If an object with mass m is dropped from rest, one...Ch. 6.8 - If an initial amount A0 of money is invested at an...Ch. 6.8 - Light enters the eye through the pupil and strikes...Ch. 6.8 - Some populations initially grow exponentially but...Ch. 6.8 - A metal cable has radius r and is covered by...Ch. 6.8 - In Section 4.3 we investigated the Fresnel...Ch. 6.8 - Suppose that the temperature in a long thin rod...Ch. 6.8 - The first appearance in print of 1Hospitals Rule...Ch. 6.8 - The figure shows a sector of a circle with central...Ch. 6.8 - Evaluate limx[xx2ln(1+xx)]Ch. 6.8 - Suppose f is a positive function. If limxaf(x) and...Ch. 6.8 - If f is continuous, f(2)=0, and f(2)=7, evaluate...Ch. 6.8 - For what values of a and b is the following...Ch. 6.8 - If f is continuous, use lHospitals Rule to show...Ch. 6.8 - If f is continuous, show that...Ch. 6.8 - Let f(x)={e1/x2ifx00ifx0 a Use the definition of...Ch. 6.8 - Let f(x)={|x|xifx01ifx=0 a Show that f is...Ch. 6.R - a What is a one-to-one function? How can you tell...Ch. 6.R - a What are the domain and range of the natural...Ch. 6.R - a How is the inverse sine function f(x)=sin1x...Ch. 6.R - Write the definitions of the hyperbolic functions...Ch. 6.R - State the derivative of each function. a y=ex b...Ch. 6.R - a How is the number e defined? b Express e as a...Ch. 6.R - a Write a differential equation that expresses the...Ch. 6.R - a What does lHospitals rule say? b How can you use...Ch. 6.R - State whether each of the following limit forms is...Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - The graph of f is shown. Is f one-to-one? Explain.Ch. 6.R - The graph of g is given. a Why is g one-to-one? b...Ch. 6.R - Suppose f is one-to-one, f(7)=(3), and f(7)=8....Ch. 6.R - Find the inverse function of f(x)=x+12x+1.Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - Let b1. For large values of x, which of the...Ch. 6.R - 11-12 Find the exact value of each expression. a...Ch. 6.R - 11-12 Find the exact value of each expression. a...Ch. 6.R - 13-20 Solve the equation for x. lnx=13Ch. 6.R - 13-20 Solve the equation for x. ex=13Ch. 6.R - 13-20 Solve the equation for x. eex=17Ch. 6.R - 13-20 Solve the equation for x. ln(1+ex)=3Ch. 6.R - 13-20 Solve the equation for x. ln(x+1)+ln(x1)=1Ch. 6.R - 13-20 Solve the equation for x. log5(cx)=dCh. 6.R - 13-20 Solve the equation for x. tan1x=1Ch. 6.R - 13-20 Solve the equation for x. sinx=0.3Ch. 6.R - 21-47 Differentiate. f(t)=t2lntCh. 6.R - 21-47 Differentiate. g(t)=et1+etCh. 6.R - 21-47 Differentiate. h()=etan2Ch. 6.R - 21-47 Differentiate. h(u)=10uCh. 6.R - 21-47 Differentiate. y=ln|sec5x+tan5x|Ch. 6.R - 21-47 Differentiate. y=xcos1xCh. 6.R - 21-47 Differentiate. y=xtan1(4x)Ch. 6.R - 21-47 Differentiate. y=emxcosnxCh. 6.R - 21-47 Differentiate. y=ln(sec2x)Ch. 6.R - 21-47 Differentiate. y=tln(t4)Ch. 6.R - 21-47 Differentiate. y=e1/xx2Ch. 6.R - 21-47 Differentiate. y=(arcsin2x)2Ch. 6.R - 21-47 Differentiate. y=3xlnxCh. 6.R - 21-47 Differentiate. y=ecosx+cos(ex)Ch. 6.R - 21-47 Differentiate. H(v)=vtanv1Ch. 6.R - 21-47 Differentiate. F(z)=log10(1+z2)Ch. 6.R - 21-47 Differentiate. y=xsinh(x2)Ch. 6.R - 21-47 Differentiate. y=(cosx)xCh. 6.R - 21-47 Differentiate. y=lnsinx12sin2xCh. 6.R - 21-47 Differentiate. y=arctan(arcsinx)Ch. 6.R - 21-47 Differentiate. y=ln(1x)+1lnxCh. 6.R - 21-47 Differentiate. xey=y1Ch. 6.R - 21-47 Differentiate. y=ln(cosh3x)Ch. 6.R - 21-47 Differentiate. y=(x2+1)4(2x+1)3(3x1)5Ch. 6.R - 21-47 Differentiate. y=cosh1(sinhx)Ch. 6.R - 21-47 Differentiate. y=xtanh1xCh. 6.R - 21-47 Differentiate. y=cos(etan3x)Ch. 6.R - Show that ddx(12tan1x+14ln(x+1)2x2+1)=1(1+x)(1+x2)Ch. 6.R - 49-52 Find f in terms of g f(x)=eg(x)Ch. 6.R - 49-52 Find f in terms of g f(x)=g(ex)Ch. 6.R - 49-52 Find f in terms of g f(x)=ln|g(x)|Ch. 6.R - 49-52 Find f in terms of g f(x)=g(lnx)Ch. 6.R - 53-54 Find f(n)(x). f(x)=2xCh. 6.R - 53-54 Find f(n)(x). f(x)=ln(2x)Ch. 6.R - Use mathematical induction to show that if...Ch. 6.R - Find y if y=x+arctanyCh. 6.R - 57-58 Find an equation of the tangent to the curve...Ch. 6.R - 57-58 Find an equation of the tangent to the curve...Ch. 6.R - At what point on the curve y=[ln(x+4)]2 is the...Ch. 6.R - If f(x)=xesinx, find f(x). Graph f and f on the...Ch. 6.R - a Find an equation of the tangent to the curve...Ch. 6.R - The function C(t)=K(eatebt),a, b, and K are...Ch. 6.R - 63-78 Evaluate the limit. limxe3xCh. 6.R - 63-78 Evaluate the limit. limxln(100x2)Ch. 6.R - 63-78 Evaluate the limit. limx3e2/(x3)Ch. 6.R - 63-78 Evaluate the limit. limxarctan(x3x)Ch. 6.R - 63-78 Evaluate the limit. limx0+ln(sinhx)Ch. 6.R - 63-78 Evaluate the limit. limxexsinxCh. 6.R - 63-78 Evaluate the limit. limx1+2x12xCh. 6.R - 63-78 Evaluate the limit. limx(1+4x)xCh. 6.R - 63-78 Evaluate the limit. limx0ex1tanxCh. 6.R - 63-78 Evaluate the limit. limx01cosxx2+xCh. 6.R - 63-78 Evaluate the limit. limx0e2xe2xln(x+1)Ch. 6.R - 63-78 Evaluate the limit. limxe2xe2xln(x+1)Ch. 6.R - 63-78 Evaluate the limit. limx(x2x3)e2xCh. 6.R - 63-78 Evaluate the limit. limx0+x2lnxCh. 6.R - 63-78 Evaluate the limit. limx1+(xx11lnx)Ch. 6.R - 63-78 Evaluate the limit. limx(/2)(tanx)cosxCh. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - Investigate the family of curves given by...Ch. 6.R - Investigate the family of functions...Ch. 6.R - An equation of motion of the form s=Aectcos(t+)...Ch. 6.R - a Show that there is exactly one root of the...Ch. 6.R - A bacteria culture contains 200 cells initially...Ch. 6.R - Cobalt-60 has a half-life of 5.24 years. a Find...Ch. 6.R - The biologist G. F. Gause conducted an experiment...Ch. 6.R - 92-105 Evaluate the integral. 04116+t2dtCh. 6.R - 92-105 Evaluate the integral. 01ye2y2dyCh. 6.R - 92-105 Evaluate the integral. 25dr1+2rCh. 6.R - 92-105 Evaluate the integral. 01ex1+e2xdxCh. 6.R - 92-105 Evaluate the integral. 0/2cosx1+sin2xdxCh. 6.R - 92-105 Evaluate the integral. exxdxCh. 6.R - 92-105 Evaluate the integral. sin(lnx)xdxCh. 6.R - 92-105 Evaluate the integral. x+1x2+2xdxCh. 6.R - 92-105 Evaluate the integral. csc2x1+cotxdxCh. 6.R - 92-105 Evaluate the integral. tanxln(cosx)dxCh. 6.R - 92-105 Evaluate the integral x1x4dxCh. 6.R - 92-105 Evaluate the integral 2tansec2dCh. 6.R - 92-105 Evaluate the integral sinhauduCh. 6.R - 92-105 Evaluate the integral (1xx)2dxCh. 6.R - 106-108 Use properties of integrals to prove the...Ch. 6.R - 106-108 Use properties of integrals to prove the...Ch. 6.R - 106-108 Use properties of integrals to prove the...Ch. 6.R - 109-110 Find f(x). f(x)=1xessdsCh. 6.R - 109-110 Find f(x). f(x)=lnx2xet2dtCh. 6.R - Find the average value of the function f(x)=1/x on...Ch. 6.R - Find the area of the region bounded by the curves...Ch. 6.R - Find the volume of the solid obtained by rotating...Ch. 6.R - If f(x)=x+x2+ex, find (f1)(1).Ch. 6.R - If f(x)=lnx+tan1x, find (f1)(/4).Ch. 6.R - What is the area of the largest rectangle in the...Ch. 6.R - What is the area of the largest triangle in the...Ch. 6.R - Evaluate 01exdxwithout using the Fundamental...Ch. 6.R - If, F(x)=abtxdt, where a, b0, then, by the...Ch. 6.R - Show that cos{arctan[sin(arccotx)]}=x2+1x2+2Ch. 6.R - If f is a continuous function such that...Ch. 6.R - The figure shows two regions in the first...Ch. 6.P - If a rectangle has its base on the x-axis and two...Ch. 6.P - Prove that log25 is an irrational number.Ch. 6.P - Does the function f(x)=e10|x2|x2 have an absolute...Ch. 6.P - If 04e(x2)4dx=k, find the value of 04xe(x2)4dx.Ch. 6.P - Show that dndxn(eaxsinbx)=rneaxsin(bx+n) where a...Ch. 6.P - Show that sin1(tanhx)=tan1(sinhx).Ch. 6.P - Show that, for x0, x1+x2tan1xxCh. 6.P - Suppose f is continuous, f(0)=0,f(1)=1,f(x)0, and...Ch. 6.P - Show that f(x)=1x1+t3dt is one-one and find...Ch. 6.P - If y=xa212a21arctansinxa+a21+cosx Show that...Ch. 6.P - For what value of a is the following equation...Ch. 6.P - Evaluate limx(x+2)1/xx1/x(x+3)1/xx1/xCh. 6.P - Evaluate. Assume that the integrand is defined and...Ch. 6.P - Sketch the set of all points (x,y) such that...Ch. 6.P - Prove that cosh(sinhx)sinh(coshx) for all xCh. 6.P - Show that, for all positive value of x and y,...Ch. 6.P - For what value of k does the equation e2x=kx have...Ch. 6.P - For which positive numbers a is it true that ax1+x...Ch. 6.P - For which positive numbers a does the curve y=ax...Ch. 6.P - For what values of c does the curve y=cx3+ex have...

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