By James Stewart
Luck on your calculus path begins right here! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, exact, and jam-packed with correct, real-world examples. With CALCULUS, 6th version, Stewart conveys not just the application of calculus that will help you increase technical competence, but additionally provides an appreciation for the intrinsic fantastic thing about the topic. His sufferer examples and integrated studying aids can assist you construct your mathematical self belief and attain your objectives within the path!
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Additional resources for Calculus: Solution Manual (5th Edition)
3 New Functions from Old Functions f g 1+x (x)= 1 x , D=[ 1,1) . We must exclude x=1 since it would make f undefined. g 33. f (x)=x , g(x)=1/x 3 2 34. f (x)=x , g(x)= x 2 35. f (x)=2x x ; g(x)=3x+2 . D=R for both f and g , and hence for their composites. 2 2 2 ( f g)(x)= f (g(x))= f (3x+2)=2(3x+2) (3x+2)=2(9x +12x+4) 3x 2=18x +21x+6 . 2 2 2 2 2 (g f )(x)=g( f (x))=g(2x x)=3(2x x)+2=6x 3x+2 . 2 2 4 3 2 2 4 3 ( f f )(x)= f ( f (x))= f (2x x)=2(2x x) (2x x)=2(4x 4x +x ) 2x +x=8x 8x +x .
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. 7. 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. 8. No horizontal line intersects the graph of f more than once. Thus, by the Horizontal Line Test, f is one to one.
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 , ... , 94 . But 94 94 2 2 2 2 sin 45 n =sin 47 n 2 n =sin n 2 n 94 94 94 94 2 2 =sin ( n ) cos 2 n cos ( n ) sin 2 n [ Subtraction 94 94 formula for the sine] 2 2 2 =0 cos 2 n ( 1)sin 2 n = sin 2 n , n=0 , 94 94 94 1 , ...
Calculus: Solution Manual (5th Edition) by James Stewart