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Unformatted text preview: Math 124 Exam 2 Oct. 10, 2006 SOLUTIONS Directions 1. SHOW YOUR WORK and be thorough in your solutions. Partial credit will only be given for work shown. 2. Any numerical answers should be left in exact form, i.e, no decimal approximations. 3. You may use calculators. Good luck! 1) [21 points] Find the derivatives of each of the following functions with respect to the variable indicated. There is no need to simplify your answers. (a) f ( x ) = 2 x 3 1 2 x with respect to x. (b) g ( t ) = 2 t 3 t 2 + w t 2 with respect to t. (c) h ( r ) = r + r + e with respect to r. (d) k ( x ) = (2 x 3 + e x ) 3 2 x 3 + 1 with respect to x. (e) w ( ) = sin( 2 ) with respect to . (f) f ( z ) = ( z + arctan z ) e with respect to z. (g) g ( x ) = (ln x )  ln( x ) with respect to x. Solutions: (a) f ( x ) = 2 x 3 1 2 x 1 , so f ( x ) = 6 x 2 + 1 2 x 2 (b) Rewriting g , we have g ( t ) = 2 t 1 + wt 2 , so g ( t ) = 2 2 wt 3 (c) h ( r ) = r ln + r  1 (d) Using the quotient rule, we have k ( x ) = 3(2 x 3 + e x ) 2 (6 x 2 + e x ) 2 x 3 + 1 (2 x 3 + e x ) 3 1 2 (2 x 3 + 1) 1 2 (6 x 2 ) 2 x 3 + 1 (e) Using the product rule, we have w ( ) = sin( 2 ) + cos( 2 )(2 ) (f) f ( z ) = e ( z + arctan z ) e 1 1 + 1 1 + z 2 (g) g ( x ) = (ln x )  1 1 x x  1 x 1 2) [14 points] Consider the function y = f ( x ) graphed below. Notice that f ( x ) is defined for...
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This note was uploaded on 06/16/2008 for the course MATH 124 taught by Professor Kennedy during the Spring '08 term at University of Arizona Tucson.
 Spring '08
 KENNEDY
 Calculus, Approximation

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