133exam2xsolution - Math 133 Dr Kurtz Exam 2 Name Section...

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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) 52 (2 ) (3 ) 2 3 x AB C xx x x x x =+ + +− + (b) 2 22 2 2 31 (1 ) ( 1 ) 1 ) 1 x xA B C x x x x ++ + + ++++ + D (c) 2 2 2 ) ( 25 ) 1 ( ) B x C D x xxx x 2 E + + + + + 2. (21 pts) Compute dy dx . (a) 1 sin (3 ) x ye = 1 sin 3 2 1 3 1( 3) x dy e dx x ⎛⎞ ⎜⎟ = ⎝⎠ (b) = x y 1 ln tan 1 2 2 11 1 1 1l n y 1 x x x =− ⎛⎞⎜⎟ + Alternatively, 1 tan ( ln ) y x and () 2 n y x x
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(c) ln(tanh( )) y x = 2 11 sec ( ) tanh( ) 2 yh x x x ⎛⎞ ′ = ⎜⎟ ⎝⎠ 3. (36 pts) Calculate the following integrals. (a) 1 22 1 sec 2 1 2 (2 1) 4 4 1) (2 1) 1 dx dx hx C xx x == −− ∫∫ + (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 2 1 5 x e d x x e x
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This note was uploaded on 05/24/2011 for the course MTH 133 taught by Professor Staff during the Spring '08 term at Michigan State University.

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133exam2xsolution - Math 133 Dr Kurtz Exam 2 Name Section...

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