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EXAM2 - Math 133 Dr Kurtz Exam 2 Name Section No TA...

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Math 133 Exam 2 Name___________________ Dr. Kurtz Section No.______________ TA_____________________ Instructions : Please show all of your work. Credit will not be given for answers with no supporting work. 1. (18 pts) For each rational function, determine the correct form of the partial fractions decomposition, but do not solve for the constants . (a) 3 1 ( 5)( 2) 5 2 x A B C x x x x x x = + + + + (b) 2 3 2 2 3 2 5 1 ( 1) ( 9) 1 ( 1) ( 1) 9 x x A B C Dx x x x x x x + + + = + + + + + + + + + E (c) 2 2 2 2 1 ( 2)( 1) 2 1 ( 1) A Bx C Dx E x x x x x x x x 2 + + = + + + + + + + 2. (21 pts) Compute dy dx . (a) 1 sec (5 ) x y e = 1 sec (5 ) 2 1 5 5 (5 ) 1 x y e x x ′ = (b) ( ) 1 3 sin ln( ) y x = ( ) 2 3 2 3 1 1 3 1 ln( ) y x x x ′ = Note: One can also write ( ) ( ) 1 3 1 sin ln( ) sin 3ln y x = = x , in which case we get 2 1 3 1 (3ln ) y x x ′ =
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