 By James Stewart

ISBN-10: 0495011606

ISBN-13: 9780495011606

Good fortune on your calculus direction starts off right here! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, exact, and choked with correct, real-world examples. With CALCULUS, 6th variation, Stewart conveys not just the software of calculus that will help you improve technical competence, but additionally promises an appreciation for the intrinsic fantastic thing about the topic. His sufferer examples and integrated studying aids can help you construct your mathematical self assurance and attain your objectives within the path!

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Extra info for Calculus: Solution Manual (5th Edition)

Example text

For sin x to be defined, we must have sin x 0 x 0,  2 ,3   2 ,   4 ,5   4 , 3  ... , so D= { x| x 2n , +2n ,where n is an integer} . 10 Stewart Calculus ET 5e 0534393217;1. 3 New Functions from Old Functions ( f  f ) (x)= f ( f (x))= f ( sin x ) =sin ( sin x ) , D=R . ( g g) (x)=g(g(x))=g ( 1 x ) =1 1 x , D={ x 0|1 x 0} ={ x 0|1 x } ={ x 0| x 1} =[0,1] . 2 38. f (x)=1 3x , D=R ; g(x)=5x +3x+2 , D=R . ( f  g) (x) = f ( g(x) ) = f (5x2+3x+2)=1 3(5x2+3x+2) 2 2 =1 15x  9x 6= 15x  9x 5 , D=R .

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) . 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 .

0 6 0 0 0 8 Stewart Calculus ET 5e 0534393217;1. 3 New Functions from Old Functions Connecting the points ( x,f(x)+g(x) ) with a smooth curve gives an approximation to the graph of f +g . Extra points can be plotted between those listed above if necessary. 30. First note that the domain of f +g is the intersection of the domains of f and g ; that is, f +g is only defined where both f and g are defined. 5 in the table above) can be added as needed. 3 2 2 31. f (x)=x +2x ; g(x)=3x  1 . D=R for both f and g .