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Unformatted text preview: Math 1110 Prelim 2 Answers Please find below abbreviated answers to the questions on the second prelim. On several of the questions, more explanation would be necessary to receive full credit. 1. ( 20 points ) For each of the following functions, determine the derivative with respect to x . (a) ( 4 points ) f ( x ) = x 1 / 3 (b) ( 4 points ) f ( x ) = log 10 2 (c) ( 4 points ) f ( x ) = tan(sin(4 x )) (d) ( 4 points ) f ( x ) = xe x + e 3 x (e) ( 4 points ) f ( x ) = 4 x ln x Solution (a) f ( x ) = 1 3 x 2 / 3 (b) f ( x ) = 0 (c) f ( x ) = 4cos(4 x )sec 2 (sin(4 x )) (d) f ( x ) = e x xe x + 3 e 3 x (e) f ( x ) = 4 ln x 4 (ln x ) 2 2. ( 15 points ) For each of the following functions, determine the derivative with respect to x . (a) ( 5 points ) f ( x ) = x tan( x ) (b) ( 5 points ) f ( x ) = e sin( x ) (c) ( 5 points ) f ( x ) = csc( x )tan( x ) Solution: (a) f ( x ) = x tan x (sec 2 ( x )ln x + tan x x ) (b) f ( x ) = 1 2 x cos( x ) e sin( x ) (c) f ( x ) = sec( x )tan( x ) 3. ( 15 points ) Find the slope of the tangent line to the curve y 2 + xy = sin( xy...
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This note was uploaded on 03/01/2012 for the course MATH 1110 at Cornell University (Engineering School).
 '06
 MARTIN,C.

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