Calculus (MindTap Course List)
8th Edition
ISBN: 9781285740621
Author: James Stewart
Publisher: Cengage Learning
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Chapter 6.3Star, Problem 80E
To determine
To graph : The function
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Chapter 6 Solutions
Calculus (MindTap Course List)
Ch. 6.1 - a What is one-to-one function? b How can you tell...Ch. 6.1 - a Suppose f is a one-to-one function with domain A...Ch. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 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 - Prob. 19ECh. 6.1 - The graph of f is given. a Why is f one-to-one? b...Ch. 6.1 - Prob. 21ECh. 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 - Prob. 24ECh. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 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 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Find (f1)(a). f(x)=3x3+4x2+6x+5,a=5Ch. 6.1 - Prob. 40ECh. 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 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - If f(x)=3x1+t3dt, find (f1)(0).Ch. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 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 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 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 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Compare the functions f(x)=x10 and g(x)=ex by...Ch. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - 23-30 Find the limit. limx(1.001)xCh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 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 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - 31-50 Differentiate the function. f(x)=x2exx2+exCh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - 31-50 Differentiate the function. f(t)=eatsinbtCh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Prob. 63ECh. 6.2 - A researcher is trying to determine the doubling...Ch. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - Prob. 70ECh. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.2 - Prob. 73ECh. 6.2 - Prob. 74ECh. 6.2 - Prob. 75ECh. 6.2 - Prob. 76ECh. 6.2 - Prob. 77ECh. 6.2 - Prob. 78ECh. 6.2 - Prob. 79ECh. 6.2 - Prob. 80ECh. 6.2 - 80-81 Draw a graph of f that shows all the...Ch. 6.2 - Prob. 82ECh. 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 - Prob. 94ECh. 6.2 - Prob. 95ECh. 6.2 - Prob. 96ECh. 6.2 - Prob. 97ECh. 6.2 - Prob. 98ECh. 6.2 - Prob. 99ECh. 6.2 - Prob. 100ECh. 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 - Prob. 104ECh. 6.2 - Prob. 105ECh. 6.2 - Prob. 106ECh. 6.2 - Prob. 107ECh. 6.2 - Prob. 108ECh. 6.2 - Prob. 109ECh. 6.2 - Prob. 110ECh. 6.2 - Prob. 111ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - 20-22 Use formula 7 to graph the given functions...Ch. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - 23-24 Make a rough sketch of the graph of each...Ch. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Prob. 40ECh. 6.3 - Prob. 41ECh. 6.3 - Prob. 42ECh. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - If a bacteria population starts with 100 bacteria...Ch. 6.3 - Prob. 46ECh. 6.3 - 47-52 Find the limit. limx3+In(x29)Ch. 6.3 - Prob. 48ECh. 6.3 - Prob. 49ECh. 6.3 - Prob. 50ECh. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - Prob. 57ECh. 6.3 - Prob. 58ECh. 6.3 - Prob. 59ECh. 6.3 - Prob. 60ECh. 6.3 - Prob. 61ECh. 6.3 - Prob. 62ECh. 6.3 - Prob. 63ECh. 6.3 - Prob. 64ECh. 6.3 - Prob. 65ECh. 6.3 - Prob. 66ECh. 6.3 - Prob. 67ECh. 6.3 - Prob. 68ECh. 6.3 - Prob. 69ECh. 6.3 - Prob. 70ECh. 6.3 - Prob. 71ECh. 6.3 - Prob. 72ECh. 6.3 - Prob. 73ECh. 6.3 - Prob. 74ECh. 6.4 - Explain why the natural logarithmic function y=lnx...Ch. 6.4 - Prob. 2ECh. 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 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 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 - Prob. 52ECh. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - Prob. 54ECh. 6.4 - Prob. 55ECh. 6.4 - Prob. 56ECh. 6.4 - Prob. 57ECh. 6.4 - Prob. 58ECh. 6.4 - Prob. 59ECh. 6.4 - 59-60 Use a graph to estimate the roots of the...Ch. 6.4 - Prob. 61ECh. 6.4 - Prob. 62ECh. 6.4 - Prob. 63ECh. 6.4 - Prob. 64ECh. 6.4 - Prob. 65ECh. 6.4 - Prob. 66ECh. 6.4 - Prob. 67ECh. 6.4 - Prob. 68ECh. 6.4 - Prob. 69ECh. 6.4 - The table gives the US population from 1790 to...Ch. 6.4 - 71-82 Evaluate the integral. 243xdxCh. 6.4 - Prob. 72ECh. 6.4 - 71-82 Evaluate the integral. 12dt83tCh. 6.4 - Prob. 74ECh. 6.4 - 71-82 Evaluate the integral. 1ex2+x+1xdxCh. 6.4 - Prob. 76ECh. 6.4 - 71-82 Evaluate the integral. (lnx)22dxCh. 6.4 - Prob. 78ECh. 6.4 - 71-82 Evaluate the integral. sin2x1+cos2xdxCh. 6.4 - Prob. 80ECh. 6.4 - 71-82 Evaluate the integral. 042sdsCh. 6.4 - Prob. 82ECh. 6.4 - Prob. 83ECh. 6.4 - Prob. 84ECh. 6.4 - Prob. 85ECh. 6.4 - Prob. 86ECh. 6.4 - Prob. 87ECh. 6.4 - Prob. 88ECh. 6.4 - Prob. 89ECh. 6.4 - Prob. 90ECh. 6.4 - Prob. 91ECh. 6.4 - Prob. 92ECh. 6.4 - Prob. 93ECh. 6.4 - Prob. 94ECh. 6.2Star - Prob. 1ECh. 6.2Star - Prob. 2ECh. 6.2Star - Prob. 3ECh. 6.2Star - Prob. 4ECh. 6.2Star - Prob. 5ECh. 6.2Star - Prob. 6ECh. 6.2Star - Prob. 7ECh. 6.2Star - Prob. 8ECh. 6.2Star - Prob. 9ECh. 6.2Star - Prob. 10ECh. 6.2Star - Prob. 11ECh. 6.2Star - Prob. 12ECh. 6.2Star - Prob. 13ECh. 6.2Star - Prob. 14ECh. 6.2Star - 15-16 Find the limit. limx3+ln(x29)Ch. 6.2Star - Prob. 16ECh. 6.2Star - Prob. 17ECh. 6.2Star - Prob. 18ECh. 6.2Star - Prob. 19ECh. 6.2Star - Prob. 20ECh. 6.2Star - Prob. 21ECh. 6.2Star - Prob. 22ECh. 6.2Star - 17-36 Differentiate the function. f(x)=sinxln(5x)Ch. 6.2Star - Prob. 24ECh. 6.2Star - Prob. 25ECh. 6.2Star - Prob. 26ECh. 6.2Star - 17-36 Differentiate the function....Ch. 6.2Star - Prob. 28ECh. 6.2Star - 17-36 Differentiate the function. F(t)=(lnt)2sintCh. 6.2Star - Prob. 30ECh. 6.2Star - 17-36 Differentiate the function. f(u)=lnu1+ln(2u)Ch. 6.2Star - Prob. 32ECh. 6.2Star - Prob. 33ECh. 6.2Star - Prob. 34ECh. 6.2Star - 17-36 Differentiate the function. y=tan[ln(ax+b)]Ch. 6.2Star - Prob. 36ECh. 6.2Star - Prob. 37ECh. 6.2Star - Prob. 38ECh. 6.2Star - Prob. 39ECh. 6.2Star - Prob. 40ECh. 6.2Star - Prob. 41ECh. 6.2Star - Prob. 42ECh. 6.2Star - Prob. 43ECh. 6.2Star - Prob. 44ECh. 6.2Star - Prob. 45ECh. 6.2Star - Prob. 46ECh. 6.2Star - Prob. 47ECh. 6.2Star - Prob. 48ECh. 6.2Star - Prob. 49ECh. 6.2Star - Prob. 50ECh. 6.2Star - Prob. 51ECh. 6.2Star - Prob. 52ECh. 6.2Star - Prob. 53ECh. 6.2Star - Prob. 54ECh. 6.2Star - Prob. 55ECh. 6.2Star - Prob. 56ECh. 6.2Star - Prob. 57ECh. 6.2Star - Prob. 58ECh. 6.2Star - Prob. 59ECh. 6.2Star - Prob. 60ECh. 6.2Star - Prob. 61ECh. 6.2Star - Prob. 62ECh. 6.2Star - Prob. 63ECh. 6.2Star - Prob. 64ECh. 6.2Star - Prob. 65ECh. 6.2Star - Prob. 66ECh. 6.2Star - Prob. 67ECh. 6.2Star - Prob. 68ECh. 6.2Star - 65-74 Evaluate the integral. 1ex2+x+1xdxCh. 6.2Star - Prob. 70ECh. 6.2Star - Prob. 71ECh. 6.2Star - Prob. 72ECh. 6.2Star - Prob. 73ECh. 6.2Star - Prob. 74ECh. 6.2Star - Prob. 75ECh. 6.2Star - Prob. 76ECh. 6.2Star - Prob. 77ECh. 6.2Star - Prob. 78ECh. 6.2Star - Prob. 79ECh. 6.2Star - Prob. 80ECh. 6.2Star - Prob. 81ECh. 6.2Star - Prob. 82ECh. 6.2Star - Prob. 83ECh. 6.2Star - a Find an equation of the tangent line to the...Ch. 6.2Star - Prob. 85ECh. 6.2Star - Prob. 86ECh. 6.2Star - Prob. 87ECh. 6.2Star - Prob. 88ECh. 6.2Star - Prob. 89ECh. 6.3Star - Sketch, by hand, the graph of the function f(x)=ex...Ch. 6.3Star - Prob. 2ECh. 6.3Star - Prob. 3ECh. 6.3Star - Prob. 4ECh. 6.3Star - Prob. 5ECh. 6.3Star - Prob. 6ECh. 6.3Star - Prob. 7ECh. 6.3Star - Solve each equation for x. a ln(lnx)=1b eex=10Ch. 6.3Star - Prob. 9ECh. 6.3Star - Prob. 10ECh. 6.3Star - Prob. 11ECh. 6.3Star - Prob. 12ECh. 6.3Star - Prob. 13ECh. 6.3Star - Prob. 14ECh. 6.3Star - Prob. 15ECh. 6.3Star - Prob. 16ECh. 6.3Star - Prob. 17ECh. 6.3Star - Prob. 18ECh. 6.3Star - Prob. 19ECh. 6.3Star - Prob. 20ECh. 6.3Star - Prob. 21ECh. 6.3Star - Prob. 22ECh. 6.3Star - Prob. 23ECh. 6.3Star - Prob. 24ECh. 6.3Star - Prob. 25ECh. 6.3Star - Prob. 26ECh. 6.3Star - 27-32 Find the limit. limxe3xe3xe3x+e3xCh. 6.3Star - 27-32 Find the limit. limxex2Ch. 6.3Star - Prob. 29ECh. 6.3Star - 27-32 Find the limit. limx2e3/(2x)Ch. 6.3Star - 27-32 Find the limit. limx(e2xcosx)Ch. 6.3Star - Prob. 32ECh. 6.3Star - 33-52 Differentiate the function. f(x)=e5Ch. 6.3Star - Prob. 34ECh. 6.3Star - Prob. 35ECh. 6.3Star - Prob. 36ECh. 6.3Star - 33-52 Differentiate the function. y=eax3Ch. 6.3Star - Prob. 38ECh. 6.3Star - 33-52 Differentiate the function. y=etanCh. 6.3Star - Prob. 40ECh. 6.3Star - 33-52 Differentiate the function. f(x)=x2exx2+exCh. 6.3Star - Prob. 42ECh. 6.3Star - 33-52 Differentiate the function. y=x2e3xCh. 6.3Star - Prob. 44ECh. 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 - Prob. 48ECh. 6.3Star - 33-52 Differentiate the function. g(u)=esecu2Ch. 6.3Star - Prob. 50ECh. 6.3Star - 33-52 Differentiate the function. y=cos(1e2x1+e2x)Ch. 6.3Star - Prob. 52ECh. 6.3Star - Prob. 53ECh. 6.3Star - Prob. 54ECh. 6.3Star - Prob. 55ECh. 6.3Star - Prob. 56ECh. 6.3Star - Prob. 57ECh. 6.3Star - Prob. 58ECh. 6.3Star - Prob. 59ECh. 6.3Star - Prob. 60ECh. 6.3Star - Prob. 61ECh. 6.3Star - Prob. 62ECh. 6.3Star - Prob. 63ECh. 6.3Star - Prob. 64ECh. 6.3Star - Prob. 65ECh. 6.3Star - An object is attached to the end of a vibrating...Ch. 6.3Star - Prob. 67ECh. 6.3Star - Prob. 68ECh. 6.3Star - Prob. 69ECh. 6.3Star - Prob. 70ECh. 6.3Star - Prob. 71ECh. 6.3Star - Prob. 72ECh. 6.3Star - Prob. 73ECh. 6.3Star - Prob. 74ECh. 6.3Star - Prob. 75ECh. 6.3Star - Prob. 76ECh. 6.3Star - A drug response curve describes the level of...Ch. 6.3Star - Prob. 78ECh. 6.3Star - After the consumption of an alcoholic beverage,...Ch. 6.3Star - Prob. 80ECh. 6.3Star - Prob. 81ECh. 6.3Star - Prob. 82ECh. 6.3Star - 83-94 Evaluate the integral. 01(xe+ex)dxCh. 6.3Star - Prob. 84ECh. 6.3Star - 83-94 Evaluate the integral. 02dxexCh. 6.3Star - Prob. 86ECh. 6.3Star - 83-94 Evaluate the integral. ex1+exdxCh. 6.3Star - Prob. 88ECh. 6.3Star - Prob. 89ECh. 6.3Star - Prob. 90ECh. 6.3Star - Prob. 91ECh. 6.3Star - Prob. 92ECh. 6.3Star - Prob. 93ECh. 6.3Star - Prob. 94ECh. 6.3Star - Prob. 95ECh. 6.3Star - Prob. 96ECh. 6.3Star - Prob. 97ECh. 6.3Star - Prob. 98ECh. 6.3Star - Prob. 99ECh. 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 - Prob. 102ECh. 6.3Star - Prob. 103ECh. 6.3Star - Prob. 104ECh. 6.3Star - Prob. 105ECh. 6.3Star - Prob. 106ECh. 6.3Star - Prob. 107ECh. 6.3Star - Prob. 108ECh. 6.3Star - Prob. 109ECh. 6.3Star - Prob. 110ECh. 6.3Star - Prob. 111ECh. 6.3Star - Prob. 112ECh. 6.4Star - a Write an equation that defines bx when b is a...Ch. 6.4Star - Prob. 2ECh. 6.4Star - Prob. 3ECh. 6.4Star - Prob. 4ECh. 6.4Star - Prob. 5ECh. 6.4Star - Prob. 6ECh. 6.4Star - Prob. 7ECh. 6.4Star - Prob. 8ECh. 6.4Star - Prob. 9ECh. 6.4Star - Prob. 10ECh. 6.4Star - Prob. 11ECh. 6.4Star - Prob. 12ECh. 6.4Star - Prob. 13ECh. 6.4Star - Prob. 14ECh. 6.4Star - Prob. 15ECh. 6.4Star - Prob. 16ECh. 6.4Star - Prob. 17ECh. 6.4Star - Prob. 18ECh. 6.4Star - Prob. 19ECh. 6.4Star - Prob. 20ECh. 6.4Star - Prob. 21ECh. 6.4Star - Prob. 22ECh. 6.4Star - Prob. 23ECh. 6.4Star - Prob. 24ECh. 6.4Star - Prob. 25ECh. 6.4Star - Prob. 26ECh. 6.4Star - Prob. 27ECh. 6.4Star - Prob. 28ECh. 6.4Star - Prob. 29ECh. 6.4Star - Prob. 30ECh. 6.4Star - Prob. 31ECh. 6.4Star - Prob. 32ECh. 6.4Star - 25-42 Differentiate the function. y=xlog4sinxCh. 6.4Star - 25-42 Differentiate the function. y=log2(xlog5x)Ch. 6.4Star - Prob. 35ECh. 6.4Star - Prob. 36ECh. 6.4Star - Prob. 37ECh. 6.4Star - Prob. 38ECh. 6.4Star - Prob. 39ECh. 6.4Star - Prob. 40ECh. 6.4Star - Prob. 41ECh. 6.4Star - Prob. 42ECh. 6.4Star - Prob. 43ECh. 6.4Star - Prob. 44ECh. 6.4Star - Prob. 45ECh. 6.4Star - Prob. 46ECh. 6.4Star - Prob. 47ECh. 6.4Star - Prob. 48ECh. 6.4Star - Prob. 49ECh. 6.4Star - Prob. 50ECh. 6.4Star - Prob. 51ECh. 6.4Star - Prob. 52ECh. 6.4Star - Prob. 53ECh. 6.4Star - Prob. 54ECh. 6.4Star - Prob. 55ECh. 6.4Star - Prob. 56ECh. 6.4Star - Prob. 57ECh. 6.4Star - Prob. 58ECh. 6.4Star - Prob. 59ECh. 6.4Star - Prob. 60ECh. 6.4Star - After the consumption of an alcoholic beverage,...Ch. 6.4Star - In this section we modeled the world population...Ch. 6.4Star - Prob. 63ECh. 6.4Star - A researcher is trying to determine the doubling...Ch. 6.4Star - Prob. 65ECh. 6.4Star - Prob. 66ECh. 6.4Star - Prob. 67ECh. 6.4Star - Prob. 68ECh. 6.4Star - Prob. 69ECh. 6.4Star - Prob. 70ECh. 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 - Prob. 7ECh. 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 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Dinosaur fossils are too old to be reliably dated...Ch. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - A roast turkey is taken from an oven when its...Ch. 6.5 - Prob. 16ECh. 6.5 - When a cold drink is taken from a refrigerator,...Ch. 6.5 - Prob. 18ECh. 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 - Prob. 21ECh. 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 - Prob. 2ECh. 6.6 - Find the exact value of each expression. a csc12 b...Ch. 6.6 - Prob. 4ECh. 6.6 - Find the exact value of each expression. a...Ch. 6.6 - Prob. 6ECh. 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 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - Prob. 12ECh. 6.6 - Prob. 13ECh. 6.6 - 12-14 Simplify the each expression. sin(2arccosx)Ch. 6.6 - Prob. 15ECh. 6.6 - Prob. 16ECh. 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 - Prob. 19ECh. 6.6 - Prove that ddt(sec1x)=1xx21Ch. 6.6 - Prob. 21ECh. 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 - Prob. 32ECh. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Prob. 34ECh. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Prob. 36ECh. 6.6 - Prob. 37ECh. 6.6 - Prob. 38ECh. 6.6 - Prob. 39ECh. 6.6 - Prob. 40ECh. 6.6 - Prob. 41ECh. 6.6 - Prob. 42ECh. 6.6 - Prob. 43ECh. 6.6 - Prob. 44ECh. 6.6 - Prob. 45ECh. 6.6 - Prob. 46ECh. 6.6 - Prob. 47ECh. 6.6 - A painting in an art gallery has height h and is...Ch. 6.6 - Prob. 49ECh. 6.6 - Prob. 50ECh. 6.6 - Prob. 51ECh. 6.6 - Prob. 52ECh. 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 - Prob. 56ECh. 6.6 - Prob. 57ECh. 6.6 - Prob. 58ECh. 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 - Prob. 68ECh. 6.6 - Prob. 69ECh. 6.6 - Prob. 70ECh. 6.6 - Prob. 71ECh. 6.6 - Prob. 72ECh. 6.6 - Prob. 73ECh. 6.6 - Prove that, for xy1,arctanx+arctany=arctanx+y1xy...Ch. 6.6 - Prob. 75ECh. 6.6 - Prob. 76ECh. 6.6 - Prob. 77ECh. 6.6 - Prove the identity arcsinx1x+1=2arctanx2Ch. 6.6 - Prob. 79ECh. 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 - Prob. 4ECh. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - Prob. 6ECh. 6.7 - Prob. 7ECh. 6.7 - Prob. 8ECh. 6.7 - Prob. 9ECh. 6.7 - Prob. 10ECh. 6.7 - Prob. 11ECh. 6.7 - Prob. 12ECh. 6.7 - Prob. 13ECh. 6.7 - 7-19 Prove the identity...Ch. 6.7 - Prob. 15ECh. 6.7 - Prob. 16ECh. 6.7 - Prob. 17ECh. 6.7 - Prob. 18ECh. 6.7 - Prob. 19ECh. 6.7 - Prob. 20ECh. 6.7 - Prob. 21ECh. 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 - Prob. 25ECh. 6.7 - Prob. 26ECh. 6.7 - Prob. 27ECh. 6.7 - Prob. 28ECh. 6.7 - Prove the formulas given in Table 6 for the...Ch. 6.7 - Prob. 30ECh. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - Prob. 32ECh. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - Prob. 34ECh. 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 - Prob. 38ECh. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - Prob. 40ECh. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - Prob. 42ECh. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - Prob. 44ECh. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - Prob. 46ECh. 6.7 - Prob. 47ECh. 6.7 - The Gateway Arch in St. Louis was designed by Eero...Ch. 6.7 - Prob. 49ECh. 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 - Prob. 53ECh. 6.7 - Prob. 54ECh. 6.7 - a Show that any function of the form...Ch. 6.7 - Prob. 56ECh. 6.7 - At what point of the curve y=coshx does the...Ch. 6.7 - Prob. 58ECh. 6.7 - Prob. 59ECh. 6.7 - Prob. 60ECh. 6.7 - 59-67 Evaluate the integral. sinhxxdxCh. 6.7 - Prob. 62ECh. 6.7 - 59-67 Evaluate the integral. coshxcosh2x1dxCh. 6.7 - Prob. 64ECh. 6.7 - 59-67 Evaluate the integral. 461t29dtCh. 6.7 - Prob. 66ECh. 6.7 - 59-67 Evaluate the integral. ex1e2xdxCh. 6.7 - Prob. 68ECh. 6.7 - Prob. 69ECh. 6.7 - Prob. 70ECh. 6.7 - Show that if a0 and b0, then there exist numbers ...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - Prob. 2ECh. 6.8 - 1-4 Given that...Ch. 6.8 - Prob. 4ECh. 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 - Prob. 8ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 10ECh. 6.8 - Prob. 11ECh. 6.8 - Prob. 12ECh. 6.8 - Prob. 13ECh. 6.8 - Prob. 14ECh. 6.8 - Prob. 15ECh. 6.8 - Prob. 16ECh. 6.8 - Prob. 17ECh. 6.8 - Prob. 18ECh. 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 - Prob. 21ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 23ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 25ECh. 6.8 - Prob. 26ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 28ECh. 6.8 - Prob. 29ECh. 6.8 - Prob. 30ECh. 6.8 - Prob. 31ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 33ECh. 6.8 - Prob. 34ECh. 6.8 - Prob. 35ECh. 6.8 - Prob. 36ECh. 6.8 - Prob. 37ECh. 6.8 - Prob. 38ECh. 6.8 - Prob. 39ECh. 6.8 - Prob. 40ECh. 6.8 - Prob. 41ECh. 6.8 - Prob. 42ECh. 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 - Prob. 45ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 47ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 49ECh. 6.8 - Prob. 50ECh. 6.8 - Prob. 51ECh. 6.8 - Prob. 52ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 54ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 56ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 58ECh. 6.8 - Prob. 59ECh. 6.8 - Prob. 60ECh. 6.8 - Prob. 61ECh. 6.8 - Prob. 62ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 64ECh. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - Prob. 66ECh. 6.8 - Prob. 67ECh. 6.8 - Prob. 68ECh. 6.8 - Prob. 69ECh. 6.8 - Prob. 70ECh. 6.8 - Prob. 71ECh. 6.8 - Prob. 72ECh. 6.8 - Prob. 73ECh. 6.8 - Prob. 74ECh. 6.8 - Prob. 75ECh. 6.8 - Prob. 76ECh. 6.8 - Prob. 77ECh. 6.8 - Prob. 78ECh. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - Prob. 80ECh. 6.8 - Prob. 81ECh. 6.8 - Prob. 82ECh. 6.8 - 83-85 a Graph the function. b Use lHospitals Rule...Ch. 6.8 - Prob. 84ECh. 6.8 - Prob. 85ECh. 6.8 - Prob. 86ECh. 6.8 - Prob. 87ECh. 6.8 - If an object with mass m is dropped from rest, one...Ch. 6.8 - Prob. 89ECh. 6.8 - Prob. 90ECh. 6.8 - Prob. 91ECh. 6.8 - Prob. 92ECh. 6.8 - Prob. 93ECh. 6.8 - Prob. 94ECh. 6.8 - Prob. 95ECh. 6.8 - The figure shows a sector of a circle with central...Ch. 6.8 - Prob. 97ECh. 6.8 - Suppose f is a positive function. If limxaf(x) and...Ch. 6.8 - Prob. 99ECh. 6.8 - Prob. 100ECh. 6.8 - Prob. 101ECh. 6.8 - Prob. 102ECh. 6.8 - Prob. 103ECh. 6.8 - Prob. 104ECh. 6.R - a What is a one-to-one function? How can you tell...Ch. 6.R - Prob. 2CCCh. 6.R - a How is the inverse sine function f(x)=sin1x...Ch. 6.R - Prob. 4CCCh. 6.R - Prob. 5CCCh. 6.R - a How is the number e defined? b Express e as a...Ch. 6.R - Prob. 7CCCh. 6.R - Prob. 8CCCh. 6.R - State whether each of the following limit forms is...Ch. 6.R - Prob. 1TFQCh. 6.R - Prob. 2TFQCh. 6.R - Prob. 3TFQCh. 6.R - Prob. 4TFQCh. 6.R - Prob. 5TFQCh. 6.R - Prob. 6TFQCh. 6.R - Prob. 7TFQCh. 6.R - Prob. 8TFQCh. 6.R - Prob. 9TFQCh. 6.R - Prob. 10TFQCh. 6.R - Prob. 11TFQCh. 6.R - Determine whether the statement is true or false....Ch. 6.R - Prob. 13TFQCh. 6.R - Prob. 14TFQCh. 6.R - Prob. 15TFQCh. 6.R - Prob. 16TFQCh. 6.R - Prob. 17TFQCh. 6.R - Prob. 18TFQCh. 6.R - Prob. 19TFQCh. 6.R - Prob. 1ECh. 6.R - Prob. 2ECh. 6.R - Prob. 3ECh. 6.R - Prob. 4ECh. 6.R - Prob. 5ECh. 6.R - Prob. 6ECh. 6.R - Prob. 7ECh. 6.R - Prob. 8ECh. 6.R - Prob. 9ECh. 6.R - Prob. 10ECh. 6.R - Prob. 11ECh. 6.R - Prob. 12ECh. 6.R - Prob. 13ECh. 6.R - Prob. 14ECh. 6.R - Prob. 15ECh. 6.R - Prob. 16ECh. 6.R - Prob. 17ECh. 6.R - Prob. 18ECh. 6.R - Prob. 19ECh. 6.R - 13-20 Solve the equation for x. sinx=0.3Ch. 6.R - Prob. 21ECh. 6.R - Prob. 22ECh. 6.R - Prob. 23ECh. 6.R - 21-47 Differentiate. h(u)=10uCh. 6.R - Prob. 25ECh. 6.R - Prob. 26ECh. 6.R - Prob. 27ECh. 6.R - 21-47 Differentiate. y=emxcosnxCh. 6.R - Prob. 29ECh. 6.R - 21-47 Differentiate. y=tln(t4)Ch. 6.R - Prob. 31ECh. 6.R - Prob. 32ECh. 6.R - Prob. 33ECh. 6.R - 21-47 Differentiate. y=ecosx+cos(ex)Ch. 6.R - Prob. 35ECh. 6.R - Prob. 36ECh. 6.R - Prob. 37ECh. 6.R - 21-47 Differentiate. y=(cosx)xCh. 6.R - Prob. 39ECh. 6.R - Prob. 40ECh. 6.R - Prob. 41ECh. 6.R - 21-47 Differentiate. xey=y1Ch. 6.R - Prob. 43ECh. 6.R - Prob. 44ECh. 6.R - Prob. 45ECh. 6.R - Prob. 46ECh. 6.R - Prob. 47ECh. 6.R - Prob. 48ECh. 6.R - Prob. 49ECh. 6.R - Prob. 50ECh. 6.R - Prob. 51ECh. 6.R - Prob. 52ECh. 6.R - Prob. 53ECh. 6.R - Prob. 54ECh. 6.R - Prob. 55ECh. 6.R - Prob. 56ECh. 6.R - Prob. 57ECh. 6.R - Prob. 58ECh. 6.R - Prob. 59ECh. 6.R - Prob. 60ECh. 6.R - Prob. 61ECh. 6.R - Prob. 62ECh. 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 - Prob. 71ECh. 6.R - 63-78 Evaluate the limit. limx01cosxx2+xCh. 6.R - Prob. 73ECh. 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 - Prob. 77ECh. 6.R - 63-78 Evaluate the limit. limx(/2)(tanx)cosxCh. 6.R - Prob. 79ECh. 6.R - Prob. 80ECh. 6.R - Prob. 81ECh. 6.R - Prob. 82ECh. 6.R - Prob. 83ECh. 6.R - Prob. 84ECh. 6.R - Prob. 85ECh. 6.R - Prob. 86ECh. 6.R - Prob. 87ECh. 6.R - Prob. 88ECh. 6.R - Prob. 89ECh. 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 - Prob. 92ECh. 6.R - Prob. 93ECh. 6.R - Prob. 94ECh. 6.R - Prob. 95ECh. 6.R - Prob. 96ECh. 6.R - Prob. 97ECh. 6.R - 92-105 Evaluate the integral. sin(lnx)xdxCh. 6.R - Prob. 99ECh. 6.R - Prob. 100ECh. 6.R - Prob. 101ECh. 6.R - Prob. 102ECh. 6.R - Prob. 103ECh. 6.R - 92-105 Evaluate the integral sinhauduCh. 6.R - Prob. 105ECh. 6.R - Prob. 106ECh. 6.R - Prob. 107ECh. 6.R - Prob. 108ECh. 6.R - Prob. 109ECh. 6.R - Prob. 110ECh. 6.R - Prob. 111ECh. 6.R - Prob. 112ECh. 6.R - Prob. 113ECh. 6.R - Prob. 114ECh. 6.R - Prob. 115ECh. 6.R - What is the area of the largest rectangle in the...Ch. 6.R - Prob. 117ECh. 6.R - Prob. 118ECh. 6.R - Prob. 119ECh. 6.R - Prob. 120ECh. 6.R - Prob. 121ECh. 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 - Prob. 3PCh. 6.P - Prob. 4PCh. 6.P - Prob. 5PCh. 6.P - Prob. 6PCh. 6.P - Prob. 7PCh. 6.P - Prob. 8PCh. 6.P - Prob. 9PCh. 6.P - Prob. 10PCh. 6.P - Prob. 11PCh. 6.P - Prob. 12PCh. 6.P - Prob. 13PCh. 6.P - Sketch the set of all points (x,y) such that...Ch. 6.P - Prob. 15PCh. 6.P - Prob. 16PCh. 6.P - Prob. 17PCh. 6.P - Prob. 18PCh. 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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