Ws21 - WORKSHEET 21 Fall 1995 1 Find f(x in terms of g(x and g(x where g(x > 0 for all x(Recall If c is a constant then g(c is a constant a f(x =

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WORKSHEET 21 - Fall 1995 1. Find f 0 ( x )intermso f g ( x )and g 0 ( x ), where g ( x ) > 0 for all x . (Recall: If c is a constant, then g ( c )is a constant.) a) f ( x )= g ( x )( x a ) b) f ( x )= g ( a )( x a ) c) f ( x )= g ( x + g ( x )) d) f ( x )= g ( x ) x a e) f ( x )= 1 g ( x ) f) f ( x )= g ( xg ( a )) g) f ( x )= p g ( x ) 2 h) f ( x )= p g ( x 2 ) i) f (2 x +3)= g ( x 2 ) 2. Suppose that f ( a )= g ( a )= h ( a ), that f ( x ) g ( x ) h ( x ) for all x ,andthat f 0 ( a )= h 0 ( a ). a) Prove that g ( x ) is di±erentiable at a ,andthat f 0 ( a )= g 0 ( a )= h 0 ( a ). (Hint: Begin with the de²nition of g 0 ( a ). The Squeeze Theorem may be useful.) b) Show that the conclusion does not follow if we omit the hypothesis f ( a )= g ( a )= h ( a ). c) Draw a graph illustrating part a). d) Draw a graph illustrating part b). e) Useparta)toshowthati f g ( x )= ± x 2 sin 1 x ,x 6 =0; 0 ,x =0 then g 0 (0) = 0. (Hint: Use
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.

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Ws21 - WORKSHEET 21 Fall 1995 1 Find f(x in terms of g(x and g(x where g(x > 0 for all x(Recall If c is a constant then g(c is a constant a f(x =

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