371_James Stewart Calculus 5 Edition Answers

371_James Stewart Calculus 5 Edition Answers - Stewart...

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Unformatted text preview: Stewart Calculus ET 5e 0534393217;4. Applications of Differentiation; 4.3 How Derivatives Affect the Shape of a Graph 52. (a) f is periodic with period ( x 2 ) lim ln tan x = ( /2 ) ( 2 (b) f (x)=ln tan x ( , and x ) , so we consider only / f ( x )= 2 2tan xsec x 2 0, and decreasing on 2 (c) No maximum or minimum 2 4 / (d) f (x)= = sin xcos x sin 2x and 0, 4 4 < x< 4 2 f ,0 // 2 , so x=0 , x= ( 2 ) . lim ln tan x = x 2 , 0 are VA. 2 sec x =2 >0 tan x tan x>0 0<x< , so f is increasing on 2 . (x)= 8cos 2x 2 <0 sin 2x , so f is CD on , and CU on ) lim ln tan x = + ( /2 ) tan x cos 2x>0 2 2 < x< 2 , 4 4 and ,0 , 42 . IP are 4 ,0 . (e) 53. (a) From the graph, we get an estimate of f (1) 1.41 as a local maximum value, and no local minimum value. x+1 / 1x f ( x )= f ( x )= . 3/2 2 2 x +1 x +1 ( ) 23 ...
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