Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Calculus (MindTap Course List)
26E27E28E29E30EUse the given graph of f to sketch the graph of f1.Use the given graph of f to sketch the graph of f1.33E34E35E36E37E38EFind (f1)(a). f(x)=3x3+4x2+6x+5,a=540EFind (f1)(a). f(x)=3+x2+tan(x/2),1x1,a=3Find (f1)(a). f(x)=x3+4x+4,a=343E44EIf f(x)=3x1+t3dt, find (f1)(0).46E47E48E49E50Ea Write an equation that defines the exponential function with base h0. b What is the domain of this function? c If b1, what is the range of this function? d Sketch the general shape of the graph of the exponential function for each of the following cases. i b1 ii b=1 iii 0b1a How is the number e defined? b What is an approximate value for e? c What is the natural exponential function?3E4E5E6E7E8E9E10E11E12E13EStarting with the graph of y=ex, find the equation of the graph that results from a reflecting about the line y=4. b reflecting about the line x=2.Find the domain of each function. a f(x)=1ex21e1x2 b f(x)=1+xecosx16E17E18E19E20ECompare the functions f(x)=x10 and g(x)=ex by graphing both f and g in several viewing rectangles. When does the graph of g finally surpass the graph of f?22E23E23-30 Find the limit. limx(1.001)x25E26E27E28E29E30E31-50 Differentiate the function. f(x)=e531-50 Differentiate the function. k(r)=er+re31-50 Differentiate the function. f(x)=(3x25x)ex31-50 Differentiate the function. y=ex1ex31-50 Differentiate the function. y=eax331-50 Differentiate the function. g(x)=ex2x37E38E31-50 Differentiate the function. f(x)=x2exx2+ex40E41E42E31-50 Differentiate the function. f(t)=eatsinbt44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63EA researcher is trying to determine the doubling time for a population of the bacterium Giardia lamblia. He starts a culture in a nutrient solution and estimates the bacteria count every four hours. His data are shown in the table. Time hours 0 4 8 12 16 20 24 Bacteria count CFU/mL 37 47 63 78 105 130 173 a Make a scatter plot of the data. b Use a graphing calculator to find an exponential curve f(t)=abt that models the bacteria population t hours later. c Graph the model from part b together with the scatter plot in part a Use the TRACE feature to determine how long it takes for the bacteria count to double.65E66E67E68E69E70E71E72E73E74E75E76E77E78E79E80E80-81 Draw a graph of f that shows all the important aspects of the curve. Estimate the local maximum and minimum values and then use calculus to find these values exactly. Use a graph of f to estimate the inflection points. f(x)=ex3x82E83-94 Evaluate the integral. 01(xe+ex)dx83-94 Evaluate the integral. 55edx83-94 Evaluate the integral. 02dxex83-94 Evaluate the integral. x2ex3dx83-94 Evaluate the integral. ex1+exdx83-94 Evaluate the integral. (1+ex)2exdx83-94 Evaluate the integral. (ex+ex)2dx83-94 Evaluate the integral. ex(4+ex)5dx83-94 Evaluate the integral. eu(1eu)2du83-94 Evaluate the integral. esincosd83-94 Evaluate the integral. 12e1/xx2dx94E95E96E97E98E99E100EAn oil storage tank ruptures at time t=0 and oil leaks from the tank at a rate of r(t)=100e0.01t liters per minute. How much oil leaks out during the first hour?A bacteria population starts with 400 bacteria and grows at a rate of r(t)=(450.268)e1.12567t bacteria per hour. How many bacteria will there be after three hours?Dialysis treatment removes urea and other waste products from a patients blood by diverting some of the bloodflow externally through a machine called a dialyzer. The rate at which urea is removed from the blood in mg/min is often well described by the equation u(t)=rvC0ert/V where r is the rate of flow of blood through the dialyzer in mL/min, V is the volume of the patients blood in mL, and C0 is the amount of urea in the blood in mg at time t=0. Evaluate the integral 030u(t)dt and interpret it.104E105E106E107E108E109E110E111E1E2E3E4E5E6E7E8E9E10E11E12E13E14E15-16 Find the limit. limx3+ln(x29)16E17E18E19E20E21E22E17-36 Differentiate the function. f(x)=sinxln(5x)24E25E26E17-36 Differentiate the function. G(y)=ln(2y+1)5y2+128E17-36 Differentiate the function. F(t)=(lnt)2sint30E17-36 Differentiate the function. f(u)=lnu1+ln(2u)32E33E34E17-36 Differentiate the function. y=tan[ln(ax+b)]36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E65-74 Evaluate the integral. 1ex2+x+1xdx70E71E72E73E74E75E76E77E78E79E80E81E82E83Ea Find an equation of the tangent line to the curve y=1/t that is parallel to the secant line AD. b Use part a to show that In 20.66.85E86E87E88E89E1E2E3E4E5E3-8 Find the exact value of each expression. a log1.52.25 b log54log55007E8E9E10E11E12E13E14E15E16E17E18E19E20-22 Use formula 7 to graph the given functions on a common screen. How are these graphs related? y=log2x, y=log4x, y=log6x, y=log8x21E22E23E23-24 Make a rough sketch of the graph of each function. Do not use a calculator. Just use the graphs given in Figures 2 and 3 and, if necessary, the transformations of Section 1.3. a y=ln(x) b y=ln|x|25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44EIf a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n=f(t)=1002t/3. a Find the inverse of this function and explain its meaning. b When will the population reach 50, 000?46E47-52 Find the limit. limx3+In(x29)48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72E73E74ESketch, by hand, the graph of the function f(x)=ex with particular attention to how the graph crosses the y-axis. What fact allows you to do this?