133exam2asolution

# 133exam2asolution - 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 tan (5 ) x ye = 1 tan 2 1 5 1( 5) x dy e dx x ⎛⎞ = ⎜⎟ + ⎝⎠ (b) 1 1 ln sin y x = 2 2 1 11 1 1 sin 1 dy dx x x x =− 1 (c) sinh(ln cos ) yx = 1 cosh(ln cos ) ( sin ) cos dy x x dx x

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3. (36 pts) Calculate the following integrals. (a) 2 (0 3) 12 4 dx x xx < < 2 9( 2 3 ) dx x = −− 3 23 2 a ux du dx = ⎛⎞ ⎜⎟ =− = ⎝⎠ 1 22 11 sin 3 3 du u C u == + 1 12 3 sin x C =+ (b) 2 3 0 cos x xdx π D i f f I n t 3 x cos x 2 3 x sin x 6 x cos x 6 sin x 0 cos x () 2 33 2 2 0 0 3 3 cos sin 3 cos 6 sin 6cos 06 0 0006 3 6 8 x x x x x x x x ππ ⎡⎤ ⎣⎦ = +− + − ++− = − +
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133exam2asolution - Math 133 Dr Kurtz Exam 2 Name Section...

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