By James Stewart
Good fortune on your calculus path begins right here! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, actual, and full of appropriate, real-world examples. With CALCULUS, 6th variation, Stewart conveys not just the software of calculus that will help you strengthen technical competence, but additionally delivers an appreciation for the intrinsic great thing about the topic. His sufferer examples and integrated studying aids might help you construct your mathematical self assurance and accomplish your ambitions within the path!
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Extra info for Calculus: Solution Manual (5th Edition)
Sample text
1 x 2 2 1 . So f (x)=ln is x >1 . 2 30. y= f (x)= x +2x , x>0 2 x 1 x+1 . Interchange x and y : y=ln ( 2) 2 4 1 y 2 1 2 2 y>0 and y =x +2x = 1 1 2 2 x +2x y =0 . Now we use the quadratic formula: 2 1+y . But x>0 , so the negative root is inadmissible. Interchange x 2 and y : y= 1+ 1+x . So f (x)= 1+ 1+x , x>0 . 31. The function f is one to one, so its inverse exists and the graph of its inverse can be obtained by reflecting the graph of f about the line y=x . 4 Stewart Calculus ET 5e 0534393217;1.
3 22. We see that the graphs of f (x)=x and g(x)=4x 1 intersect three times. 86 . 3 Alternatively, we could find these values by finding the zeros of h(x)=x 4x+1 . 2 23. We see that the graphs of f (x)=x and g(x)=sin x intersect twice. One solution is x=0. The other solution of f =g is the x coordinate of the point of intersection in the first quadrant. 88. Alternatively, we could 2 find that value by finding the positive zero of h(x)=x sin x . 8 Stewart Calculus ET 5e 0534393217;1. 88 by using the following keystrokes: .
4 Graphing Calculators and Computers 2 / / 32. f (x)= 1+cx . If c<0 , the function is only defined on 1 c ,1 c , and its graph is the top half of an ellipse. If c=0 , the graph is the line y=1 . If c>0 , the graph is the top half of a hyperbola. As c approaches 0 , these curves become flatter and approach the line y=1 . n x 33. y=x 2 . As n increases, the maximum of the function moves further from the origin, and gets larger. Note, however, that regardless of n , the function approaches 0 as x .