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) 31 (5 ) (2 ) 5 2 x AB C xx x x x x =+ + +− + (b) 2 32 2 3 2 51 (1 ) ( 9 ) 1 ) ) 9 x xA B C D x x x x x ++ + + + + + E (c) 22 2 2 1 ) ( 1 ) 2 1 ( 1 ) x C D x E x x 2 + + + + + + + 2. (21 pts) Compute dy dx . (a) 1 sec (5 ) x ye = 1 sec (5 ) 2 1 5 5( 5 ) 1 x ⎛⎞ ⎜⎟ ′ = ⎝⎠ (b) () 13 sin ln( ) yx = 2 3 2 3 11 3 1l n y x x x ′ = Note: One can also write ( ) ( ) 1 sin ln( ) sin 3ln y x −− == x , in which case we get 2 1( 3 l n) y x x ′ =
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(c) 2 sinh( ) x y e = 22 cosh( ) 2 xx ye e ′ = x 3. (36 pts) Calculate the following integrals. (a) (2 1) 4 4 1) (2 1) 1 dx dx x = −− ∫∫ Setting 21 ux = , gives 2 du dx = 11 2 1 sec sec 2 1 2 1 du uC x C uu =+ = + (b) 1 0 x x ed x Diff Int 2 2 2 1 2 2 1 2 4 1 0 8 x x x x xe x e e e 1 1 2 2 2 2 2 2 222 0 0 1 1 1 1 4 2 2 4 4 4 4 x x x
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This note was uploaded on 05/12/2008 for the course MATH 133 taught by Professor Wei during the Spring '07 term at Michigan State University.

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EXAM2 - Math 133 Dr. Kurtz Exam 2 Name_ Section No._ TA_...

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