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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781305270343

Chapter 3.5, Problem 30E

Textbook Problem

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

**30.**

Single Variable Calculus: Early Transcendentals, Volume I

Ch. 3.1 - (a) How is the number e defined? (b) Use a...Ch. 3.1 - (a) Sketch, by hand, the graph of the function...Ch. 3.1 - Differentiate the function. f(x) = 240Ch. 3.1 - Differentiate the function. f(x) = e5Ch. 3.1 - Differentiate the function. f(x) = 5.2x + 2.3Ch. 3.1 - Differentiate the function. g(x)=74x23x+12Ch. 3.1 - Differentiate the function. f(t) = 2t3 3t2 4tCh. 3.1 - Differentiate the function. f(t) = 1.4t5 2.5t2+...Ch. 3.1 - Differentiate the function. g(x) = x2(1 2x)Ch. 3.1 - Differentiate the function. H(u) = (3u 1)(u + 2)

Ch. 3.1 - Differentiate the function. g(t) = 2t3/4Ch. 3.1 - Differentiate the function. B(y) = cy6Ch. 3.1 - Differentiate the function. F(r)=5r3Ch. 3.1 - Differentiate the function. y = x5/3 x2/3Ch. 3.1 - Differentiate the function. R(a) = (3a + 1)2Ch. 3.1 - Differentiate the function. h(t)=t44etCh. 3.1 - Differentiate the function. S(p)=ppCh. 3.1 - Differentiate the function. y=x3(2+x)Ch. 3.1 - Differentiate the function. y=3ex+4x3Ch. 3.1 - Differentiate the function. S(R) = 4R2Ch. 3.1 - Differentiate the function. h(u)=Au3+Bu2+CuCh. 3.1 - Differentiate the function. y=x+xx2Ch. 3.1 - Differentiate the function. y=x2+4x+3xCh. 3.1 - Differentiate the function. G(t)=5t+7tCh. 3.1 - Differentiate the function. j(x) = x2.4 + e2.4Ch. 3.1 - Differentiate the function. k(r) = er + reCh. 3.1 - Differentiate the function. G(q) = (1 + q1)2Ch. 3.1 - Differentiate the function. F(z)=A+Bz+Cz2z2Ch. 3.1 - Differentiate the function. f(v)=v32vevvCh. 3.1 - Differentiate the function. D(t)=1+16t2(4t)3Ch. 3.1 - Differentiate the function. z=Ay10+BeyCh. 3.1 - Differentiate the function. y = ex + 1 + 1Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find equations of the tangent line and normal line...Ch. 3.1 - Find equations of the tangent line and normal line...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find f'(x). Compare the graphs of f and f' and use...Ch. 3.1 - Find f'(x). Compare the graphs of f and f' and use...Ch. 3.1 - (a) Graph the function f(x) = x4 3x3 6x2 + 7x +...Ch. 3.1 - (a) Graph the function g(x) = ex 3x2in the...Ch. 3.1 - Find the first and second derivatives of the...Ch. 3.1 - Find the first and second derivatives of the...Ch. 3.1 - Find the first and second derivatives of the...Ch. 3.1 - Find the first and second derivatives of the...Ch. 3.1 - The equation of motion of a particle is s = t3 ...Ch. 3.1 - The equation of motion of a particle is s = t4 ...Ch. 3.1 - Biologists have proposed a cubic polynomial to...Ch. 3.1 - The number of tree species S in a given area A in...Ch. 3.1 - Boyles Law states that when a sample of gas is...Ch. 3.1 - Find the points on the curve y = 2x3 + 3x2 12x +...Ch. 3.1 - For what value of x does the graph of f(x) = ex ...Ch. 3.1 - Show that the curve y = 2ex + 3x + 5x3 has no...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find equations of both lines that are tangent to...Ch. 3.1 - At what point on the curve y = 1 + 2ex 3x is the...Ch. 3.1 - Find an equation of the normal line to the curve...Ch. 3.1 - Where does the normal line to the parabola y = x2 ...Ch. 3.1 - Draw a diagram to show that there are two tangent...Ch. 3.1 - (a) Find equations of both lines through the point...Ch. 3.1 - Use the definition of a derivative to show that if...Ch. 3.1 - Find the nth derivative of each function by...Ch. 3.1 - Find a second-degree polynomial P such that P(2) =...Ch. 3.1 - The equation y" + y' 2y = x2 is called a...Ch. 3.1 - Find a cubic function y = ax3 + bx2 + cx + d whose...Ch. 3.1 - Find a parabola with equation y = ax2 + bx + c...Ch. 3.1 - Let {x2+1ifx1x+1ifx1 Is f differentiable at 1?...Ch. 3.1 - At what numbers is the following function g...Ch. 3.1 - (a) For what values of x is the function f(x) =...Ch. 3.1 - Where is the function h(x) = |x 1| + |x + 2|...Ch. 3.1 - Find the parabola with equation y = ax2 + bx whose...Ch. 3.1 - Suppose the curve y = x4 + ax3 + bx2 + cx + d has...Ch. 3.1 - For what values of a and b is the line 2x + y = b...Ch. 3.1 - Find the value of c such that the line y=32x+6 is...Ch. 3.1 - What is the value of c such that the line y = 2x +...Ch. 3.1 - The graph of any quadratic function f(x) = ax2 +...Ch. 3.1 - Let f(x){x2ifx2mx+bifx2 Find the values of m and b...Ch. 3.1 - A tangent line is drawn to the hyperbola xy = c at...Ch. 3.1 - Evaluate limx1x10001x1.Ch. 3.1 - Draw a diagram showing two perpendicular lines...Ch. 3.1 - If c12, how many lines through the point (0, c)...Ch. 3.1 - Sketch the parabolas y = x2 and y = x2 2x + 2. Do...Ch. 3.2 - Find the derivative of f(x) = (1 + 2x2)(x x2) in...Ch. 3.2 - Find the derivative o f the function...Ch. 3.2 - Differentiate. f(x) = (3x2 5x)exCh. 3.2 - 4. Differentiate.
Ch. 3.2 - Differentiate. y=xexCh. 3.2 - Differentiate. y=ex1exCh. 3.2 - Differentiate. g(x)=1+2x34xCh. 3.2 - Differentiate. G(x)=x222x+1Ch. 3.2 - Differentiate. H(u)=(uu)(u+u)Ch. 3.2 - Differentiate. J(v) = (v3 2v)(v4 + v2)Ch. 3.2 - Differentiate. F(y)=(1y23y4)(y+5y3)Ch. 3.2 - Differentiate. f(z) = (1 ez)(z + ez)Ch. 3.2 - Differentiate. y=x2+1x31Ch. 3.2 - Differentiate. y=x2+1Ch. 3.2 - Differentiate. y=t3+3tt24t+3Ch. 3.2 - Differentiate. y=1t3+2t21Ch. 3.2 - Differentiate. y=ep(p+pp)Ch. 3.2 - Differentiate. h(r)=aerb+erCh. 3.2 - Differentiate. y=sss2Ch. 3.2 - Differentiate. y=(z2+ez)zCh. 3.2 - Differentiate. f(t)=t3t3Ch. 3.2 - Differentiate. V(t)=4+ttetCh. 3.2 - Differentiate. f(x)=x2exx2+exCh. 3.2 - Differentiate. F(t)=AtBt2+Ct3Ch. 3.2 - Differentiate. f(x)=xx+cxCh. 3.2 - Differentiate. f(x)=ax+bcx+dCh. 3.2 - Find f'(x) and f"(x). f(x) = (x3 + 1)exCh. 3.2 - Find f'(x) and f"(x). f(x)=xexCh. 3.2 - Find f'(x) and f"(x). f(x)=x21+exCh. 3.2 - Find f'(x) and f"(x). f(x)=xx21Ch. 3.2 - Find an equation of the tangent line to the given...Ch. 3.2 - Find an equation of the tangent line to the given...Ch. 3.2 - Find equations of the tangent line and normal line...Ch. 3.2 - Find equations of the tangent line and normal line...Ch. 3.2 - (a) The curve y = 1/(1 + x2) is called a witch of...Ch. 3.2 - (a) The curve y = x/(1 + x2) is called a...Ch. 3.2 - (a) If f(x) = (x3 x)ex, find f'(x). (b) Check to...Ch. 3.2 - (a) If f(x) = ex/(2x2 + x + 1), find f'(x). (b)...Ch. 3.2 - (a) If f(x) = (x2 1)/(x2 + 1), find f'(x) and...Ch. 3.2 - (a) If f(x) = (x2 1)ex, find f'(x) and f"(x). (b)...Ch. 3.2 - If f(x) = x2/(l + x), find f"(1).Ch. 3.2 - If g(x) = x/ex. find g(n)(x).Ch. 3.2 - Suppose that f(5) = 1, f'(5) = 6, g(5) = 3, and...Ch. 3.2 - Suppose that f(4) = 2, g(4) = 5, f'(4) = 6. and...Ch. 3.2 - If f(x) = exg(x), where g(0) = 2 and g'(0) = 5,...Ch. 3.2 - If h(2) = 4 and h'(2) = 3, find ddx(h(x)x)|x=2Ch. 3.2 - If g(x) = xf(x), where f(3) = 4 and f'(3) = 2,...Ch. 3.2 - If f(2) = 10 and f'(x) = x2f(x) for all x, find...Ch. 3.2 - If f and g are the functions whose graphs are...Ch. 3.2 - Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F...Ch. 3.2 - If g is a differentiable function, find an...Ch. 3.2 - If f is a differentiable function, find an...Ch. 3.2 - How many tangent lines to the curve y = x/(x + 1)...Ch. 3.2 - Find equations of the tangent lines to the curve...Ch. 3.2 - Find R'(0), where R(x)=x3x3+5x51+3x3+6x6+9x9 Hint:...Ch. 3.2 - Use the method of Exercise 55 to compute Q'(0),...Ch. 3.2 - In this exercise we estimate the rate at which the...Ch. 3.2 - A manufacturer produces bolts of a fabric with a...Ch. 3.2 - The Michaelis-Menten equation for the enzyme...Ch. 3.2 - The biomass B(t) of a fish population is the total...Ch. 3.2 - (a) Use the Product Rule twice to prove that if f,...Ch. 3.2 - (a) If F(x) = f(x) g(x), where f and g have...Ch. 3.2 - Find expressions for the first five derivatives of...Ch. 3.2 - (a) If g is differentiable, the Reciprocal Rule...Ch. 3.3 - Differentiate. f(x) = x2 sin xCh. 3.3 - Differentiate. f(x) = x cos x + 2 tan xCh. 3.3 - Differentiate. f(x) = ex cos xCh. 3.3 - Differentiate. y = 2 sec x csc xCh. 3.3 - Differentiate. y = sec tanCh. 3.3 - Differentiate. g() = e(tan )Ch. 3.3 - Differentiate. y = c cos t + t2 sin tCh. 3.3 - Differentiate. f(t)=cottetCh. 3.3 - Differentiate. y=x2tanxCh. 3.3 - Differentiate. y = sin cosCh. 3.3 - Differentiate f()=sin1+cosCh. 3.3 - Differentiate. y=cosx1sinxCh. 3.3 - Differentiate. y=tsint1+tCh. 3.3 - Differentiate. y=sint1+tantCh. 3.3 - Differentiate. f() = cos sinCh. 3.3 - Differentiate. f(t) = tet cot tCh. 3.3 - Prove that ddx(cscx)=cscxcotx.Ch. 3.3 - Prove that ddx(secx)=secxtanxCh. 3.3 - Prove that ddx(cotx)=csc2x.Ch. 3.3 - Prove, using the definition of derivative. that if...Ch. 3.3 - Find an equation of the tangent line to the curve...Ch. 3.3 - Find an equation of the tangent line to the curve...Ch. 3.3 - Find an equation of the tangent line to the curve...Ch. 3.3 - Find an equation of the tangent line to the curve...Ch. 3.3 - (a) Find an equation of the tangent line to the...Ch. 3.3 - (a) Find an equation of the tangent line to the...Ch. 3.3 - (a) If f(x) = sec x x, find f'(x). (b) Check to...Ch. 3.3 - (a) If f(x) = ex cos x, find f'(x) and f"(x). (b)...Ch. 3.3 - If H() = sin , find H'() and H"( ).Ch. 3.3 - If f(t) = sec t, find f"(/4).Ch. 3.3 - (a) Use the Quotient Rule to differentiate the...Ch. 3.3 - Suppose f(/3) = 4 and f'(/3) = 2, and let g(x) =...Ch. 3.3 - For what values of x does the graph of f have a...Ch. 3.3 - For what values of x does the graph of f have a...Ch. 3.3 - A mass on a spring vibrates horizontally on a...Ch. 3.3 - An elastic band is hung on a hook and a mass is...Ch. 3.3 - A ladder 10 ft long rests against a vertical wall....Ch. 3.3 - An object with weight W is dragged along a...Ch. 3.3 - Find the limit. limx0sin5x3xCh. 3.3 - Find the limit. limx0sinxsinxCh. 3.3 - Find the limit. limt0tan6tsin2tCh. 3.3 - Find the limit. lim0cos1sinCh. 3.3 - Find the limit. limx0sin3x5x34xCh. 3.3 - Find the limit. limx0sin3xsin5xx2Ch. 3.3 - Find the limit. lim0sin+tanCh. 3.3 - Find the limit. limx0cscxsin(sinx)Ch. 3.3 - Find the limit. lim0cos122Ch. 3.3 - Find the limit. limx0sin(x2)xCh. 3.3 - Find the limit. limx/41tanxsinxcosxCh. 3.3 - Find the limit. limx1sin(x1)x2+x2Ch. 3.3 - Find the given derivative by finding the first few...Ch. 3.3 - Find the given derivative by finding the first few...Ch. 3.3 - Find constants A and B such that the function y =...Ch. 3.3 - (a) Evaluate limxxsin1x. (b) Evaluate limx0xsin1x....Ch. 3.3 - Differentiate each trigonometric identity to...Ch. 3.3 - A semicircle with diameter PQ sits on an isosceles...Ch. 3.3 - The figure shows a circular arc of length s and a...Ch. 3.3 - Let f(x)=x1cos2x. (a) Graph f. What type of...Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Find the derivative of the function. F(x) = (5x6 +...Ch. 3.4 - Find the derivative of the function. F (x) = (1 +...Ch. 3.4 - Find the derivative of the function. f(x)=5x+1Ch. 3.4 - Find the derivative of the function. f(x)=1x213Ch. 3.4 - Find the derivative of the function. f() = cos(2)Ch. 3.4 - Find the derivative of the function. g() = cos2Ch. 3.4 - Find the derivative of the function. y = x2e3xCh. 3.4 - Find the derivative of the function. f(t) = t sin ...Ch. 3.4 - Find the derivative of the function. f(t) = eat...Ch. 3.4 - Find the derivative of the function. g(x)=ex2xCh. 3.4 - Find the derivative of the function. f(x) = (2x ...Ch. 3.4 - Find the derivative of the function. g(x) = (x2 +...Ch. 3.4 - Find the derivative of the function. h(t) = (t +...Ch. 3.4 - Find the derivative of the function. F(t) = (3t ...Ch. 3.4 - Find the derivative of the function. y=xx+1Ch. 3.4 - Find the derivative of the function. y=(x+1x)5Ch. 3.4 - Find the derivative of the function. y = e tanCh. 3.4 - Find the derivative of the function. f(t)2t3Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function. r(t)=10t2Ch. 3.4 - Find the derivative of the function. f(z) =...Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function. J() = tan2(n)Ch. 3.4 - Find the derivative of the function. F(t) = et sin...Ch. 3.4 - Find the derivative of the function. F(t)=t2t3+1Ch. 3.4 - Find the derivative of the function. G(x) = 4C/xCh. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function. y = x2 e1/xCh. 3.4 - Find the derivative of the function. y = cot2(sin...Ch. 3.4 - Find the derivative of the function. y=1+xe2xCh. 3.4 - Find the derivative of the function. f(t) =...Ch. 3.4 - Find the derivative of the function. y = esin 2x +...Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function. y=x+x+xCh. 3.4 - Find the derivative of the function. g(x) = (2...Ch. 3.4 - Find the derivative of the function. y=234xCh. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function. y = [x + (x +...Ch. 3.4 - Find y and y. y = cos(sin 3)Ch. 3.4 - Find y and y. y=1(1+tanx)2Ch. 3.4 - Find y and y. y=1sectCh. 3.4 - Find y and y. y=eexCh. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - (a) Find an equation of the tangent line to the...Ch. 3.4 - (a) The curve y=|x|/2x2 is called a bullet-nose...Ch. 3.4 - (a) If f(x)=2x2x, find f(x). (b) Check to see that...Ch. 3.4 - The function f(x) = sin(x + sin 2x), 0 x ,...Ch. 3.4 - Find all points on the graph of the function f(x)...Ch. 3.4 - At what point on the curve y=1+2x is the tangent...Ch. 3.4 - If F(x) = f(g(x)), where f(2) = 8, f(2) = 4, f(5)...Ch. 3.4 - If h(x)=4+3f(x), where f(1) = 7andf(1) = 4, find...Ch. 3.4 - A table of values for f, g, f, and g is given. (a)...Ch. 3.4 - Let f and g be the functions in Exercise 63. (a)...Ch. 3.4 - If f and g are the functions whose graphs are...Ch. 3.4 - If f is the function whose graph is shown, let...Ch. 3.4 - If g(x)=f(x), where the graph off is shown,...Ch. 3.4 - Suppose f is differentiable on and is a real...Ch. 3.4 - Suppose f is differentiable on . Let F(x) = f(ex)...Ch. 3.4 - Let g(x) = ecx + f(x) and h(x) = ekxf(x), where...Ch. 3.4 - Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3,...Ch. 3.4 - If g is a twice differentiable function and f(x) =...Ch. 3.4 - If F(x) = f(3f(4f(x))), where f(0) = 0 and f(0) =...Ch. 3.4 - If F(x) = f(x f (xf(x))), where f(1) = 2, f(2) =...Ch. 3.4 - Show that the function y = e2x (A cos 3x + B sin...Ch. 3.4 - For what values of r does the function y = erx...Ch. 3.4 - Find the 50th derivative of y = cos 2x.Ch. 3.4 - Find the 1000th derivative of f(x) = xex.Ch. 3.4 - The displacement of a particle on a vibrating...Ch. 3.4 - If the equation of motion of a particle is given...Ch. 3.4 - A Cepheid variable star is a star whose brightness...Ch. 3.4 - In Example 1.3.4 we arrived at a model for the...Ch. 3.4 - The motion of a spring that is subject to a...Ch. 3.4 - Under certain circumstance a rumor spreads...Ch. 3.4 - The average blood alcohol concentration (BAC) of...Ch. 3.4 - In Section 1.4 we modeled the world population...Ch. 3.4 - A particle moves along a straight line with...Ch. 3.4 - Air is being pumped into a spherical weather...Ch. 3.4 - The flash unit on a camera operates by storing...Ch. 3.4 - The table gives the US population from 1790 to...Ch. 3.4 - Use the Chain Rule to prove the following. (a) The...Ch. 3.4 - Use the Chain Rule and the Product Rule to give an...Ch. 3.4 - (a) If n is a positive integer, prove that...Ch. 3.4 - Suppose y = f(x) is a curve that always lies above...Ch. 3.4 - Use the Chain Rule to show that if is measured in...Ch. 3.4 - (a) Write |x|=x2 and use the Chain Rule to show...Ch. 3.4 - lf y = f(u) and u = g(x), where f and g are twice...Ch. 3.4 - If y = f(u) and u = g(x), where f and g possess...Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - Find dy/dx by implicit differentiation. 5. x2 4xy...Ch. 3.5 - Find dy/dx by implicit differentiation. 6. 2x2 +...Ch. 3.5 - Find dy/dx by implicit differentiation. 7. x4 +...Ch. 3.5 - Find dy/dx by implicit differentiation. 8. x3 xy2...Ch. 3.5 - Find dy/dx by implicit differentiation. 9....Ch. 3.5 - Find dy/dx by implicit differentiation. 10. xey =...Ch. 3.5 - Find dy/dx by implicit differentiation. 11. y cos...Ch. 3.5 - Find dy/dx by implicit differentiation. 12....Ch. 3.5 - Find dy/dx by implicit differentiation. 13....Ch. 3.5 - Find dy/dx by implicit differentiation. 14. ey sin...Ch. 3.5 - Find dy/dx by implicit differentiation. 15. ex/y...Ch. 3.5 - Find dy/dx by implicit differentiation. 16....Ch. 3.5 - Find dy/dx by implicit differentiation. 17....Ch. 3.5 - Find dy/dx by implicit differentiation. 18. x sin...Ch. 3.5 - Find dy/dx by implicit differentiation. 19....Ch. 3.5 - Find dy/dx by implicit differentiation. 20....Ch. 3.5 - If f(x) + x2 [f(x)]3 = 10 and f(1) = 2, find f(1).Ch. 3.5 - If g(x) + x sin g(x) = x2, find g(0).Ch. 3.5 - Regard y as the independent variable and x as the...Ch. 3.5 - Regard y as the independent variable and x as the...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - (a) The curve with equation y2 = 5x4 x2 is called...Ch. 3.5 - (a) The curve with equation y2 = x3 + 3x2 is...Ch. 3.5 - Find y by implicit differentiation. 35. x2 + 4y2 =...Ch. 3.5 - Find y by implicit differentiation. 36. x2 + xy +...Ch. 3.5 - Find y by implicit differentiation. 37. sin y +...Ch. 3.5 - Find y by implicit differentiation. 38. x3 y3 = 7Ch. 3.5 - If xy + ey = e, find the value of y at the point...Ch. 3.5 - If x2 + xy + y3 = 1, find the value of y at the...Ch. 3.5 - Find the points on the lemniscate in Exercise 31...Ch. 3.5 - Show by implicit differentiation that the tangent...Ch. 3.5 - Find an equation of the tangent line to the...Ch. 3.5 - Show that the sum of the x-and y-intercepts of any...Ch. 3.5 - Show, using implicit differentiation, that any...Ch. 3.5 - The Power Rule can be proved using implicit...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find f(x). Check that your answer is reasonable by...Ch. 3.5 - Find f(x). Check that your answer is reasonable by...Ch. 3.5 - Prove the formula for (d/dx)(cos1x) by the same...Ch. 3.5 - (a) One way of defining sec1x is to say that...Ch. 3.5 - Two curves are orthogonal if their tangent lines...Ch. 3.5 - Two curves are orthogonal if their tangent lines...Ch. 3.5 - Two curves are orthogonal if their tangent lines...Ch. 3.5 - Two curves are orthogonal if their tangent lines...Ch. 3.5 - Show that the ellipse x2/a2 + y2/b2 = 1 and the...Ch. 3.5 - Find the value of the number a such that the...Ch. 3.5 - (a) The van der Waals equation for n moles of a...Ch. 3.5 - The equation x2 xy + y2 = 3 re presents a...Ch. 3.5 - (a) Where does the normal line to the ellipse x2 ...Ch. 3.5 - Find all points on the curve x2y2 + xy = 2 where...Ch. 3.5 - Find equations of both the tangent lines to the...Ch. 3.5 - (a) Suppose f is a one-to-one differentiable...Ch. 3.5 - (a) Show that f(x) = x + ex is one-to-one. (b)...Ch. 3.5 - The Bessel function of order 0, y = J(x),...Ch. 3.5 - The figure shows a lamp located three units to the...Ch. 3.6 - Explain why the natural logarithmic function y =...Ch. 3.6 - Differentiate the function. f(x) = x ln x xCh. 3.6 - Differentiate the function. f(x ) = sin(ln x)Ch. 3.6 - Differentiate the function. f(x) = ln(sin2x)Ch. 3.6 - Differentiate the function. f(x)=ln1xCh. 3.6 - Differentiate the function. y=1lnxCh. 3.6 - Differentiate the function. f(x) = log10(1 + cos...Ch. 3.6 - Differentiate the function. f(x)log10xCh. 3.6 - Differentiate the function. g(x) = ln(xe2x)Ch. 3.6 - Differentiate the function. g(t)=1+lntCh. 3.6 - Differentiate the function. F(t) =(ln t)2 sin tCh. 3.6 - Differentiate the function. h(x)=ln(x+x21)Ch. 3.6 - Differentiate the function. G(y)=ln(2y+1)5y2+1Ch. 3.6 - Differentiate the function. p(v)=lnv1vCh. 3.6 - Differentiate the function. F(s) = ln ln sCh. 3.6 - Differentiate the function. y = ln |1 + t t3|Ch. 3.6 - Differentiate the function. T(z) = 2z log2zCh. 3.6 - Differentiate the function. y = ln(csc x cot x)Ch. 3.6 - Differentiate the function. y = ln(ex + xex)Ch. 3.6 - Differentiate the function. H(z)=a2z2a2+z2Ch. 3.6 - Differentiate the function. y = tan[ln(ax + b)]Ch. 3.6 - Differentiate the function. y = log2 (x log5 x)Ch. 3.6 - Find y and y. y=xlnxCh. 3.6 - Find y and y. y=lnx1+lnxCh. 3.6 - Find y and y. y = ln |sec x|Ch. 3.6 - Find y and y. y = ln(l + ln x)Ch. 3.6 - Differentiate f and find the domain of f....Ch. 3.6 - Differentiate f and find the domain of f....Ch. 3.6 - Differentiate f and find the domain of f. f(x) =...Ch. 3.6 - Differentiate f and find the domain of f. f(x) ln...Ch. 3.6 - If f(x) = ln(x + ln x), find f(1).Ch. 3.6 - If f(x) = cos(ln x2), find f(1).Ch. 3.6 - Find an equation of the tangent line to the curve...Ch. 3.6 - Find an equation of the tangent line to the curve...Ch. 3.6 - If f(x) = sin x + ln x, find f(x). Check that your...Ch. 3.6 - Find equations of the tangent lines to the curve y...Ch. 3.6 - Let f(x) = cx + ln(cos x). For what value of c is...Ch. 3.6 - Let f(x) = logb (3x2 2). For what value of b is...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Find y if y = ln(x2 + y2).Ch. 3.6 - Find y if xy = yx.Ch. 3.6 - Find a formula for f(n)(x) if f(x) = ln(x 1).Ch. 3.6 - Find d9dx9(x8lnx).Ch. 3.6 - Use the definition of derivative to prove that...Ch. 3.6 - Show that limn(1+xn)n=exfor any x 0.Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - Graphs of the velocity functions of two particles...Ch. 3.7 - Graphs of the position functions of two particles...Ch. 3.7 - The height (in meters) of a projectile shot...Ch. 3.7 - If a ball is thrown vertically upward with a...Ch. 3.7 - If a rock is thrown vertically upward from the...Ch. 3.7 - A particle moves with position function s = t4 ...Ch. 3.7 - (a) A company makes computer chips from square...Ch. 3.7 - (a) Sodium chlorate crystals are easy to grow in...Ch. 3.7 - (a) Find the average rate of change of the area of...Ch. 3.7 - A stone is dropped into a lake, creating a...Ch. 3.7 - A spherical balloon is being inflated. Find the...Ch. 3.7 - (a) The volume of a growing spherical cell is...Ch. 3.7 - The mass of the part of a metal rod that lies...Ch. 3.7 - If a tank holds 5000 gallons of water, which...Ch. 3.7 - The quantity of charge Q in coulombs (C) that has...Ch. 3.7 - Newtons Law of Gravitation says that the magnitude...Ch. 3.7 - The force F acting on a body with mass m and...Ch. 3.7 - Some of the highest tides in the world occur in...Ch. 3.7 - Boyles Law states that when a sample of gas is...Ch. 3.7 - If, in Example 4, one molecule of the product C is...Ch. 3.7 - In Example 6 we considered a bacteria population...Ch. 3.7 - The number of yeast cells in a laboratory culture...Ch. 3.7 - The table shows how the average age of first...Ch. 3.7 - Refer to the law of laminar flow given in Example...Ch. 3.7 - The frequency of vibrations of a vibrating violin...Ch. 3.7 - Suppose that the cost (in dollars) for a company...Ch. 3.7 - The cost function for a certain commodity is C(q)...Ch. 3.7 - If p(x) is the total value of the production when...Ch. 3.7 - If R denotes the reaction of the body to some...Ch. 3.7 - Patients undergo dialysis treatment to remove urea...Ch. 3.7 - Invasive species often display a wave of advance...Ch. 3.7 - The gas law for an ideal gas at absolute...Ch. 3.7 - In a fish farm, a population of fish is introduced...Ch. 3.7 - In the study of ecosystems, predator-prey models...Ch. 3.8 - A population of protozoa develops with a constant...Ch. 3.8 - A common inhabitant of human intestines is the...Ch. 3.8 - A bacteria culture initially contains 100 cells...Ch. 3.8 - A bacteria culture grows with constant relative...Ch. 3.8 - The table gives estimates of the world population,...Ch. 3.8 - The table gives the population of Indonesia, in...Ch. 3.8 - Experiments show that if the chemical reaction...Ch. 3.8 - Strontium-90 has a half-life of 28 days. (a) A...Ch. 3.8 - The half-life of cesium-137 is 30 years. Suppose...Ch. 3.8 - A sample oflritium-3 decayed to 94.5% of its...Ch. 3.8 - Scientists can determine the age of ancient...Ch. 3.8 - Dinosaur fossils are too old to be reliably dated...Ch. 3.8 - Dinosaur fossils are often dated by using an...Ch. 3.8 - A curve passes through the point (0, 5) and has...Ch. 3.8 - A roast turkey is taken from an oven when its...Ch. 3.8 - In a murder investigation, the temperature of the...Ch. 3.8 - When a cold drink is taken from a refrigerator,...Ch. 3.8 - A freshly brewed cup of coffee has temperature 95C...Ch. 3.8 - The rate of change of atmospheric pressure P with...Ch. 3.8 - (a) If 1000 is borrowed at 8% interest, find the...Ch. 3.8 - (a) If 3000 is invested at 5% interest, find the...Ch. 3.8 - (a) How long will it take an investment to double...Ch. 3.9 - If V is the volume of a cube with edge length x...Ch. 3.9 - (a) If A is the area of a circle with radius r and...Ch. 3.9 - Each side of a square is increasing at a rate of 6...Ch. 3.9 - The length of a rectangle is increasing at a rate...Ch. 3.9 - A cylindrical tank with radius 5 m is being filled...Ch. 3.9 - The radius of a sphere is increasing at a rate of...Ch. 3.9 - The radius of a spherical ball is increasing at a...Ch. 3.9 - The area of a triangle with sides of lengths a and...Ch. 3.9 - Suppose y=2x+1, where x and y are functions of t....Ch. 3.9 - Suppose 4x2 + 9y2 = 36, where x and y are...Ch. 3.9 - If x2 + y2 + z2 = 9, dx/dt = 5, and dy/dt = 4,...Ch. 3.9 - A particle is moving along a hyperbola xy = 8. As...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - Two cars start moving from the same point. One...Ch. 3.9 - A spotlight on the ground shines on a wall 12m...Ch. 3.9 - A man starts walking north at 4 ft/s from a point...Ch. 3.9 - A baseball diamond is a square with side 90 ft. A...Ch. 3.9 - The altitude of a triangle is increasing at a rate...Ch. 3.9 - A boat is pulled into a dock by a rope attached to...Ch. 3.9 - At noon, ship A is 100 km west of ship B. Ship A...Ch. 3.9 - A particle moves along the curve y = 2 sin(x/2)....Ch. 3.9 - Water is leaking out of an inverted conical tank...Ch. 3.9 - A trough is 10 ft long and its ends have the shape...Ch. 3.9 - A water trough is 10m long and a cross-section has...Ch. 3.9 - A swimming pool is 20 ft wide, 40 ft long, 3 ft...Ch. 3.9 - Gravel is being dumped from a conveyor belt at a...Ch. 3.9 - A kite 100ft above the ground moves horizontally...Ch. 3.9 - The sides of an equilateral triangle are...Ch. 3.9 - How fast is the angle between the ladder and the...Ch. 3.9 - The top of a ladder slides down a vertical wall at...Ch. 3.9 - According to the model we used to solve Example 2,...Ch. 3.9 - If the minute hand of a clock has length r (in...Ch. 3.9 - A faucet is filling a hemispherical basin of...Ch. 3.9 - Boyles Law states that when a sample of gas is...Ch. 3.9 - When air expands adiabatically (without gaining or...Ch. 3.9 - If two resistors with resistances R1 and R2 are...Ch. 3.9 - Brain weight B as a function of body weight Win...Ch. 3.9 - Two sides of a triangle have lengths 12 m and 15...Ch. 3.9 - Two carts, A and B, are connected by a rope 39 ft...Ch. 3.9 - A television camera is positioned 4000 ft from the...Ch. 3.9 - A lighthouse is located on a small island 3 km...Ch. 3.9 - A plane flies horizontally at an altitude of 5 km...Ch. 3.9 - A Ferris wheel with a radius of 10m is rotating at...Ch. 3.9 - A plane flying with a constant speed of 300 km/h...Ch. 3.9 - Two people start from the same point. One walks...Ch. 3.9 - A runner sprints around a circular track of radius...Ch. 3.9 - The minute hand on a watch is 8 mm long and the...Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linear approximation of the function...Ch. 3.10 - Find the linear approximation of the function...Ch. 3.10 - Verify the given linear approximation at a = 0....Ch. 3.10 - Verify the given linear approximation at a = 0....Ch. 3.10 - Verify the given linear approximation at a = 0....Ch. 3.10 - Verify the given linear approximation at a = 0....Ch. 3.10 - Find the differential of each function. 11. (a) y...Ch. 3.10 - Find the differential of each function. 12. (a)...Ch. 3.10 - Find the differential of each function. 13. (a)...Ch. 3.10 - Find the differential of each function. 14. (a) y...Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Explain, in terms of linear approximations or...Ch. 3.10 - Explain, in terms of linear approximations or...Ch. 3.10 - Explain, in terms of linear approximations or...Ch. 3.10 - Let f(x) = (x 1)2 g(x) = e2x and h(x) = 1 + ln(1 ...Ch. 3.10 - The edge of a cube was found to be 30 cm with a...Ch. 3.10 - The radius of a circular disk is given as 24 cm...Ch. 3.10 - The circumference of a sphere was measured to be...Ch. 3.10 - Use differentials to estimate the amount of paint...Ch. 3.10 - (a) Use differentials to find a formula for the...Ch. 3.10 - One side of a right triangle is known to be 20 cm...Ch. 3.10 - If a current I passes through a resistor with...Ch. 3.10 - When blood flows along a blood vessel, the flux F...Ch. 3.10 - Establish the following rules for working with...Ch. 3.10 - On page 431 of Physics: Calculus, 2d ed., by...Ch. 3.10 - Suppose that the only information we have about a...Ch. 3.10 - Suppose that we dont have a formula for g(x) but...Ch. 3.11 - Find the numerical value of each expression. 1....Ch. 3.11 - Find the numerical value of each expression. 2....Ch. 3.11 - Find the numerical value of each expression. 3....Ch. 3.11 - Find the numerical value of each expression. 4....Ch. 3.11 - Find the numerical value of each expression. 5....Ch. 3.11 - Find the numerical value of each expression. 6....Ch. 3.11 - Prove the identity. 7. sinh(x) = sinh x (This...Ch. 3.11 - Prove the identity. 8. cosh(x) = cosh x (This...Ch. 3.11 - Prove the identity. 9. cosh x + sinh x = exCh. 3.11 - Prove the identity. 10. cosh x sinh r = exCh. 3.11 - Prove the identity. 11. sinh(x + y) = sinh x cosh...Ch. 3.11 - Prove the identity. 12. cosh(x + y) = cosh x cosh...Ch. 3.11 - Prove the identity. 13. coth2x 1 = csch2xCh. 3.11 - Prove the identity. 14....Ch. 3.11 - Prove the identity. 15. sinh 2x = 2 sinh x cosh xCh. 3.11 - Prove the identity. 16. cosh 2x = cosh2x + sinh2xCh. 3.11 - Prove the identity. 17. tanh(lnx)=x21x2+1Ch. 3.11 - Prove the identity. 18. 1+tanhx1tanhx=e2xCh. 3.11 - Prove the identity. 19. (cosh x + sinh x)n = cosh...Ch. 3.11 - If x=1213 find the values of the other hyperbolic...Ch. 3.11 - If cosh=53 and x 0. find the values of the other...Ch. 3.11 - (a) Use the graphs of sinh, cosh, and tanh in...Ch. 3.11 - Use the definitions of the hyperbolic functions to...Ch. 3.11 - Prove the formulas given in Table 1 for the...Ch. 3.11 - Give an alternative solution 10 Example 3 by...Ch. 3.11 - Prove Equation 4.Ch. 3.11 - Prove Equation 5 using (a) the method of Example 3...Ch. 3.11 - For each of I he following functions (i) give a...Ch. 3.11 - Prove the formulas given in Table 6 for the...Ch. 3.11 - Find the derivative. Simplify where possible. 30....Ch. 3.11 - Find the derivative. Simplify where possible. 31....Ch. 3.11 - Find the derivative. Simplify where possible. 32....Ch. 3.11 - Find the derivative. Simplify where possible. 33....Ch. 3.11 - Find the derivative. Simplify where possible. 34....Ch. 3.11 - Find the derivative. Simplify where possible. 35....Ch. 3.11 - Find the derivative. Simplify where possible. 36....Ch. 3.11 - Find the derivative. Simplify where possible. 37....Ch. 3.11 - Find the derivative. Simplify where possible. 38....Ch. 3.11 - Find the derivative. Simplify where possible. 39....Ch. 3.11 - Find the derivative. Simplify where possible. 40....Ch. 3.11 - Find the derivative. Simplify where possible. 41....Ch. 3.11 - Find the derivative. Simplify where possible. 42....Ch. 3.11 - Find the derivative. Simplify where possible. 43....Ch. 3.11 - Find the derivative. Simplify where possible. 44....Ch. 3.11 - Find the derivative. Simplify where possible. 45....Ch. 3.11 - Show that ddx1+tanhx1tanhx4=12ex/2.Ch. 3.11 - Show that ddx arctan(tanh x) = sech 2x.Ch. 3.11 - The Gateway Arch in St. Louis was designed by Eero...Ch. 3.11 - If a water wave with length L. moves with velocity...Ch. 3.11 - A flexible cable always hangs in the shape of a...Ch. 3.11 - A telephone line hangs between two poles 14 m...Ch. 3.11 - Using principles from physics it can be shown that...Ch. 3.11 - A cable with linear density = 2 kg/m is strung...Ch. 3.11 - A model for the velocity of a falling object after...Ch. 3.11 - (a) Show that any function of the form y = A sinh...Ch. 3.11 - If x = ln( sec + tan ), show that sec = cosh x.Ch. 3.11 - At what point of the curve y = cosh x does the...Ch. 3.11 - Investigate the family of functions fn(x) = tanh...Ch. 3 - State each differentiation rule both in symbols...Ch. 3 - State the derivative of each function. (a) y = xn...Ch. 3 - (a) How is the number e defined? (b) Express e as...Ch. 3 - (a) Explain how implicit differentiation works....Ch. 3 - Give several examples of how the derivative can be...Ch. 3 - (a) Write a differential equation that expresses...Ch. 3 - (a) Write an expression for the linearization of f...Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Calculate y'. 1. y = (x2 + x3)4Ch. 3 - Calculate y'. 2. y=1x1x35Ch. 3 - Calculate y'. 3. y=x2x+2xCh. 3 - Calculate y'. 4. y=tanx1+cosxCh. 3 - Calculate y'. 5. y = x2 sin xCh. 3 - Calculate y'. 6. y = x cos1xCh. 3 - Calculate y'. 7. y=t41t4+1Ch. 3 - Calculate y'. 8. xey = y sin xCh. 3 - Calculate y'. 9. y = ln(x ln x)Ch. 3 - Calculate y'. 10. y = emx' cos nxCh. 3 - Calculate y'. 11. y=xcosxCh. 3 - Calculate y'. 12. y = (arcsin 2x)2Ch. 3 - Calculate y'. 13. y=e1/xx2Ch. 3 - Calculate y'. 14. y = ln sec xCh. 3 - Calculate y'. 15. y + x cos y = x2yCh. 3 - Calculate y'. 16. y=(u1u2+u+1)4Ch. 3 - Calculate y'. 17. y=arctanCh. 3 - Calculate y'. 18. y = cot(csc x)Ch. 3 - Calculate y'. 19. y=tan(t1+t2)Ch. 3 - Calculate y'. 20. y = exsec xCh. 3 - Calculate y'. 21. y = 3x ln xCh. 3 - Calculate y'. 22. y = sec(1 + x2)Ch. 3 - Calculate y'. 23. y = (1 x1)1Ch. 3 - Calculate y'. 24. y=1/x+x3Ch. 3 - Calculate y'. 25. sin(xy) = x2 yCh. 3 - Calculate y'. 26. y=sinxCh. 3 - Calculate y'. 27. y = log5(1 + 2x)Ch. 3 - Calculate y'. 28. y = (cos x)xCh. 3 - Calculate y'. 29. y=lnsinx12sin2xCh. 3 - Calculate y'. 30. y=(x2+1)4(2x+1)3(3x1)5Ch. 3 - Calculate y'. 31. y = x tan1(4x)Ch. 3 - Calculate y'. 32. y = ecos x + cos(ex)Ch. 3 - Calculate y'. 33. y = ln | sec 5x + tan 5x |Ch. 3 - Calculate y'. 34. y = 10tanCh. 3 - Calculate y'. 35. y = cot(3x2 + 5)Ch. 3 - Calculate y'. 36. y=tln(t4)Ch. 3 - Calculate y'. 37. y=sin(tan1+x3)Ch. 3 - Calculate y'. 38. y=arctan(arcsinx)Ch. 3 - Calculate y'. 39. y = tan2(sin )Ch. 3 - Calculate y'. 40. xey = y 1Ch. 3 - Calculate y'. 41. y=x+1(2x)5(x+3)7Ch. 3 - Calculate y'. 42. y=(x+)4x4+4Ch. 3 - Calculate y'. 43. y = x sinh(x2)Ch. 3 - Calculate y'. 44. y=sinmxxCh. 3 - Calculate y'. 45. y = ln( cosh 3x)Ch. 3 - Calculate y'. 46. y=ln|x242x+5|Ch. 3 - Calculate y'. 47. y = cosh1(sinh x)Ch. 3 - Calculate y'. 48. y=xtanh1xCh. 3 - Calculate y'. 49. y=cos(etan3x)Ch. 3 - Calculate y'. 50. y=sin2(cossinx)Ch. 3 - If f(t)=4t+1 find f(2).Ch. 3 - If g() = sin , find g(/6).Ch. 3 - Find y if x6 + y6 = 1.Ch. 3 - Find f(n)(x) if f(x) = 1/(2 x).Ch. 3 - Use mathematical induction (page 72) to show that...Ch. 3 - Evaluate limt0t3tan3(2t)Ch. 3 - Find an equation of the tangent to the curve at...Ch. 3 - Find an equation of the tangent to the curve at...Ch. 3 - Find an equation of the tangent to the curve at...Ch. 3 - Find equations of the tangent line and normal line...Ch. 3 - Find equations of the tangent line and normal line...Ch. 3 - If f(x) = xesin x find f(x). Graph f and f on the...Ch. 3 - (a) If f(x)=5xx. (b) Find equations of the tangent...Ch. 3 - (a) If f(x) = 4x tan x, /2 x /2, find f and f....Ch. 3 - At what points on the curve y = sin x + cos x, 0 ...Ch. 3 - Find the points on the ellipse x2 + 2y2 = 1 where...Ch. 3 - If f(x) = (x a)(x b)(x c), show that...Ch. 3 - (a) By differentiating the double-angle formula...Ch. 3 - Suppose that f(1) = 2 f(1) = 3 f(2) = 1 f'(2) = 2...Ch. 3 - If f and g are the functions whose graphs are...Ch. 3 - Find f in terms of g. f(x) = x2g(x)Ch. 3 - Find f in terms of g. f(x) = g(x2)Ch. 3 - Find f in terms of g. f(x) = [g(x)]2Ch. 3 - Find f in terms of g. f(x) = g(g(x))Ch. 3 - Find f in terms of g. f(x) = g(ex)Ch. 3 - Find f in terms of g. f(x) = eg(x)Ch. 3 - Find f in terms of g. f(x) = ln |g(x)|Ch. 3 - Find f in terms of g. f(x) = g(ln x)Ch. 3 - Find f in terms of f and g. h(x)=f(x)g(x)f(x)+g(x)Ch. 3 - Find f in terms of f and g. h(x)=f(x)g(x)Ch. 3 - Find f in terms of f and g. h(x) = f(g(sin 4x))Ch. 3 - (a) Graph the function f(x) = x 2 sin x in the...Ch. 3 - At what point on the curve y = [ln(x + 4)]2 is the...Ch. 3 - (a) Find an equation of the tangent to the curve y...Ch. 3 - Find a parabola y = ax2 + bx + c that passes...Ch. 3 - The function C(t) = K(eat ebt), where a, b, and K...Ch. 3 - An equation of motion of the form s=Aectcos(t+)...Ch. 3 - A particle moves along a horizontal line so that...Ch. 3 - A particle moves on a vertical line so that its...Ch. 3 - The volume of a right circular cone is V=13r2h,...Ch. 3 - The mass of part of a wire is x(1+x) kilograms,...Ch. 3 - The cost, in dollars, of producing x units of a...Ch. 3 - A bacteria culture contains 200 cells initially...Ch. 3 - Cobalt-60 has a half-life of 5.24 years. (a) Find...Ch. 3 - Let C(t) be the concentration of a drug in the...Ch. 3 - A cup of hot chocolate has temperature 80C in a...Ch. 3 - The volume of a cube is increasing at a rate of...Ch. 3 - A paper cup has the shape of a cone with height 10...Ch. 3 - A balloon is rising at a constant speed of 5 ft/s....Ch. 3 - A waterskier skis over the ramp shown in the...Ch. 3 - The angle of elevation of the sun is decreasing at...Ch. 3 - (a) Find the linear approximation to f(x)=25x2...Ch. 3 - (a) Find the linearization of f(x)1+3x3 at a = 0....Ch. 3 - Evaluate dy if y = x3 2x2 + 1, x = 2, and dx =...Ch. 3 - A window has the shape of a square surmounted by a...Ch. 3 - Express the limit as a derivative and evaluate....Ch. 3 - Express the limit as a derivative and evaluate....Ch. 3 - Express the limit as a derivative and evaluate....Ch. 3 - Evaluate limx01+tanx1+sinxx3.Ch. 3 - Suppose f is a differentiable function such that...Ch. 3 - Find f(x) if it is known that ddx[f(2x)]=x2Ch. 3 - Show that the length of the portion of any tangent...Ch. 3 - Find points P and Q on the parabola y = 1 x2 so...Ch. 3 - Find the point where the curves y = x3 3x + 4 and...Ch. 3 - Show that the tangent lines to the parabola y =...Ch. 3 - Show that ddx(sin2x1+cotx+cos2x1+tanx)=cos2xCh. 3 - If f(x)=limtxsectsecxtx, find the value of f'(/4).Ch. 3 - Find the values of the constants a and b such that...Ch. 3 - Show that sin-1(tanh x) = tan1(sinh x).Ch. 3 - A car is traveling at night along a highway shaped...Ch. 3 - Prove that dndxn(sin4x+cos4x)=4n1cos(4x+n/2).Ch. 3 - If f is differentiable at a, where a 0, evaluate...Ch. 3 - The figure shows a circle with radius 1 inscribed...Ch. 3 - Find all values of r such that the parabolas y =...Ch. 3 - How many lines are tangent to both of the circles...Ch. 3 - If f(x)=x46+x45+21+x, calculate f(46)(3). Express...Ch. 3 - The figure shows a rotating wheel with radius 40...Ch. 3 - Tangent lines T1, and T2, are drawn at two points...Ch. 3 - Show that dndxn(eaxsinbx)=rneaxsin(bx+n) where a...Ch. 3 - Evaluate limxesinx1x.Ch. 3 - Let T and N be the tangent and normal lines to the...Ch. 3 - Evaluate limx0sin(3+x)2sin9x.Ch. 3 - (a) Use the identity for tan(x y) (see Equation...Ch. 3 - Let P(x1, y1) be a point on the parabola y2 = 4px...Ch. 3 - Suppose that we replace the parabolic mirror of...Ch. 3 - If f and g are differentiable functions with f(0)...Ch. 3 - Evaluate limx0sin(a+2x)2sin(a+x)+sinax2.Ch. 3 - For what value of k does the equation e2x=kx have...Ch. 3 - For which positive numbers a is it true that ax ....Ch. 3 - If y=xa212a21arctansinxa+a21+cosx show that...Ch. 3 - Given an ellipse x2/a2 + y2/b2 = 1, where a b,...Ch. 3 - Find the two points on the curve y = x4 2x2 x...Ch. 3 - Suppose that three points on the parabola y = x2...Ch. 3 - A lattice point in the plane is a point with...Ch. 3 - A cone of radius r centimeters and height h...Ch. 3 - A container in the shape of an inverted cone has...

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Multivariable Calculus

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Applied Calculus

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or gi...

Calculus: Early Transcendentals

Solving an Exponential or Logarithmic Equation In Exercises 107-118, solve for x accurate to three decimal plac...

Calculus: Early Transcendental Functions

Writing an equation of a Line In Exercises 6170, find an equation of the line that passes through the points. T...

Calculus: An Applied Approach (MindTap Course List)

Convert the expressions in Exercises 6584 to power form. 3x453x+43xx

Finite Mathematics and Applied Calculus (MindTap Course List)

A population of N = 7 scores has a mean of = 13. What is the value of X for this population?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

SOC The scores of 15 respondents on four variables are as reported here. These scores were taken from a public-...

Essentials Of Statistics

In Exercises 47-52, find and simplify f(a+h)f(a)h(h0) for each function. 51. f(x)=1x

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the curves y=9/(x2+9)...

Calculus (MindTap Course List)

Why is the coefficient of variation important? What do we mean when we say that the coefficient of variation ha...

Understanding Basic Statistics

Calculate ss. variance and standMd deviation for the following population of N "" 7 oores: s:. 1 4 3 S 3, ( N.0...

Statistics for The Behavioral Sciences (MindTap Course List)

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equ...

Single Variable Calculus

In Exercises 49 and 50, use set notation to describe the shaded region. U U

Mathematical Excursions (MindTap Course List)

Construct a probability plot that will allow you to assess the plausibility of the lognormal distribution as a ...

Probability and Statistics for Engineering and the Sciences

For Problems 2-10, state the property of equality or the property of real numbers that justifies each of the st...

Intermediate Algebra

Evaluate in problems 1-4. Write all the answers without using exponents.
2. (a) ...

Mathematical Applications for the Management, Life, and Social Sciences

Determine whether the series converges or diverges. 28. n=1e1/nn

Single Variable Calculus: Early Transcendentals

Calculate the missing information for the following purchases.
Item Selling Price Sales Tax Rate Sales Tax Exci...

Contemporary Mathematics for Business & Consumers

Complete the following tables using exact values.

Trigonometry (MindTap Course List)

Label each of the following statements as either true or false.
3. Let , , and be mappings from into such th...

Elements Of Modern Algebra

In Exercises 11 to 18, state the hypothesis and the conclusion of each statement. If you go to the game, then y...

Elementary Geometry For College Students, 7e

Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 3x...

Elementary Technical Mathematics

Testing for Continuity In Exercises 6166, describe the intervals on which the function is continuous f(x)=4x2+7...

Calculus of a Single Variable

Finding an Equation of a Tangent Line In Exercises 37-42, find an equation of the line that is tangent to the g...

Calculus: Early Transcendental Functions (MindTap Course List)

Fill in the blanks: Two matrices may be added subtracted if they both have the same . To add or subtract two ma...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Q with ABQ and CDQ, mABmCD. Also, QPABandQRCD. a How are AB and CD related? b How are QP and QR related? c H...

Elementary Geometry for College Students

Comparing Continuity In Exercises 49 and 50, discuss the continuity of the functions f and g. Explain any diffe...

Multivariable Calculus

Let F(x, y, z) = Pi + Qj + Rk have continuous first partial derivatives and E be a simple solid with boundary s...

Study Guide for Stewart's Multivariable Calculus, 8th

For y = x3 ln x, y = a) x2(1 + 3 ln x) b) x3 + 3x2 (ln x) c) 3x d) 4x2(ln x)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Find the slope of the line, if possible. x=12

College Algebra (MindTap Course List)

Explain how the mean and the standard deviation describe a distribution of scores.

Research Methods for the Behavioral Sciences (MindTap Course List)

Pessimists commonly claim that, if you drop a piece of buttered bread, it will probably land butter-side down. ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Using the Table of Block Thicknesses for a Customary Gage Block Set, determine a combination of gage blocks for...

Mathematics For Machine Technology

The mean hourly wage for employees in goods-producing industries is currently 24.57(Bureau of Labor Statistics ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Using the five class intervals 100 to 120, 120 to 140, , 180 to 200, devise a frequency distribution based on 7...

Introduction To Statistics And Data Analysis

South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York....

Statistics for Business & Economics, Revised (MindTap Course List)

MatchingIn Exercises 7176, match the equation (written in terms of cylindrical or spherical coordinates) with i...

Calculus (MindTap Course List)

Consider the following hypothesis test:
A sample of 25 provided a sample mean and a sample standard deviation...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Subtraction Versus Sign -34-9

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

In Exercises 4754, find the probability that the sum is as states when a pair of dice is rolled. a. 7or11. b. 7...

Mathematics: A Practical Odyssey

According to the National Oceanic and Atmospheric Administration (NOAA), the state ofColorado averages 18 torna...

Essentials Of Statistics For Business & Economics

In Problems 3748 find either F(s) or f(t), as indicated. 44. 1{(1+e2s)2s+2}

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

If F is a function from a set X to a set Y, then F is not one-to-one if, and only if,_________

Discrete Mathematics With Applications

For the following exercises, convert each angle in degrees to radians. Write the answer as a multiple of . 113....

Calculus Volume 1

To get on a certain toll road a driver has to take a card that lists the mile entrance paint. The card also has...

Calculus Volume 2