31_Cal_Solution of Calculus_6e

31_Cal_Solution of - f(g(x = f(cos x = cos x and g(f(x = g x = cos x C01S04.017 If f(x = sin x and g(x = x3 then f(g(x = f x3 = sin x3 = sin x3 and

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f ( g ( x )) = f (cos x )= cos x and g ( f ( x )) = g ( x ) = cos ( x ) . C01S04.017: If f ( x ) = sin x and g ( x )= x 3 , then f ( g ( x )) = f ( x 3 ) = sin ( x 3 ) = sin x 3 and g ( f ( x )) = g (sin x ) = (sin x ) 3 = sin 3 x. We note in passing that sin x 3 and sin 3 x don’t mean the same thing! C01S04.018: If f ( x ) = sin x and g ( x ) = cos x , then f ( g ( x )) = f (cos x ) = sin(cos x ) and g ( f ( x )) = g (sin x ) = cos(sin x ). C01S04.019: If f ( x )=1+ x 2 and g ( x ) = tan x , then f ( g ( x )) = f (tan x ) = 1 + (tan x ) 2 = 1 + tan 2 x and g ( f ( x )) = g (1 + x 2 ) = tan(1 + x 2 ). C01S04.020: If f ( x )=1 x 2 and g ( x ) = sin x , then f ( g ( x )) = f (sin x )=1 (sin x ) 2 =1 sin 2 x = cos 2 x and g ( f ( x )) = g (1 x 2 ) = sin(1 x 2 ) . Note: The answers to Problems 21 through 30 are not unique. We have generally chosen the simplest and most natural answer. C01S04.021:
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This note was uploaded on 09/14/2011 for the course MATH 101 taught by Professor Cheng during the Spring '11 term at Ecole Hôtelière de Lausanne.

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