By James Stewart

Good fortune on your calculus direction starts off the following! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, actual, and choked with correct, real-world examples. With CALCULUS, 6th version, Stewart conveys not just the software of calculus that can assist you enhance technical competence, but additionally offers an appreciation for the intrinsic great thing about the topic. His sufferer examples and integrated studying aids may help you construct your mathematical self assurance and attain your ambitions within the direction!

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**Sample text**

3 2 2 3 3 2 2 3 2 ( f +g)(x)=(x +2x )+(3x 1)=x +5x 1 , D=R . 2 ( f g)(x)=(x +2x ) (3x 1)=x x +1 , D=R . 3 2 2 5 4 3 2 ( fg)(x)=(x +2x )(3x 1)=3x +6x x 2x , D=R . f g 3 (x)= 2 x +2x 2 3x 1 , D= { x| x 1 3 } 2 since 3x 1 0 . 32. f (x)= 1+x , D=[ 1, ) ; g(x)= 1 x , D=( ,1] . ( f +g) (x)= 1+x + 1 x , D= ( ,1] [ 1, ) = 1,1 . ( f g) (x)= 1+x 1 x , D= 1,1 . 2 ( fg) (x)= 1+x 1 x = 1 x , D= 1,1 . 9 Stewart Calculus ET 5e 0534393217;1. 3 New Functions from Old Functions f g 1+x (x)= 1 x , D=[ 1,1) .

A) f (y)=x f (x)=y for any y in B . The domain of f (b) See the steps in (5). (c) Reflect the graph of f about the line y=x . 1 is B and the range of f 1 is A . 3. 0= f (6) . 4. f is one to one since for any two different domain values, there are different range values. 5. No horizontal line intersects the graph of f more than once. Thus, by the Horizontal Line Test, f is one to one. 6. The horizontal line y=0 (the x axis) intersects the graph of f in more than one point. Thus, by the Horizontal Line Test, f is not one to one.

But 94 94 2 2 2 2 sin 96 n =sin 94 n+2 n =sin 2 n+2 n 94 94 94 94 13 Stewart Calculus ET 5e 0534393217;1. 4 Graphing Calculators and Computers =sin 2 2 n 94 [ by periodicity of sine ], n=0 , 1 , ... , 94 So the y values, and hence the points, plotted for y=sin 96x are identical to those plotted for y=sin 2x . Note: Try graphing y=sin 94x . Can you see why all the y values are zero? 38. As in Exercise 37, we know that the points being plotted for y=sin 45x are 2 2 sin 45 n for n=0 , 1 , ...