133exam1xsolution - Math 133 Dr. Kurtz Exam 1 Name_ Section...

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Math 133 Exam 1 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. (21 pts) Compute dy dx . (a) 2 1 cos x ye x ⎛⎞ = ⎜⎟ ⎝⎠ 22 2 11 (2) c o s s i n xx x e 1 x −− =− (b) tan(ln( )) y = x or equivalently, 1 tan ln 2 y x = 2 sec (ln( )) 2 yx x x ′ = or equivalently, 2 sec ln x ′ = (c) sin (ln ) x = ln sin ln(ln ) y = cos ln(ln ) sin ln y x y =+ sin (ln ) cos ln(ln ) sin ln x x x x Alternatively, sin ln(ln ) x x = sin ln(ln ) sin cos ln(ln ) sin (ln ) cos ln(ln ) sin ln ln x y e x x x x x
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2. (21 pts) Evaluate the integrals. (a) cos(5 ) cot(5 ) sin(5 ) 11 1 ln ln sin(5 ) 55 5 x xdx dx x du uC x C u = ==+ = + ∫∫ sin(5 ) 5cos(5 ) ux du x dx = = (b) ln 2 2l n 2 23 10 0 (ln ) 1 (ln 2) 33 xu dx u du x ⎡⎤ === ⎢⎥ ⎣⎦ ln dx du x = = (c) 3 1 22 0 00 (3 ) xx x x e dx x e dx e e −− =− + 1 1 3 3 Alternatively, substitute to get 3 2 3 du x dx ⎧ =− 1 0 u edu e
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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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133exam1xsolution - Math 133 Dr. Kurtz Exam 1 Name_ Section...

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