EXAM3 - Exam 3 solutions Instructions Please show all of...

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Exam 3 solutions Instructions : Please show all of your work. Credit will not be given for answers with no supporting work. 1.(20 pts) Compute each of the improper integrals. (a) 11 22 0 00 12 1 1 1 lim lim tan 2 lim tan 2 tan 0 (1 4 ) 2 1 (2 ) 2 2 2 4 t t tt t dx dx xt xx 1 π −− →∞ →∞ →∞ ⎛⎞ == = ⎜⎟ ++ ⎝⎠ ∫∫ = (b) 1 33 1 0 lim lim 3(1 ) lim ) 3 3 ) ) t t t dx dx →→ ⎡⎤ = + ⎢⎥ −− ⎣⎦ = 2.(20 pts) Solve the initial value problem. Write y explicitly as a function of x . (a) 2 ;( 0 ) x dy ey y dx =− = 1 () 2 2 2 2 2 x dx x x x x x dy ye dx vx e e dy dx e e C C C e e y ee += = + =− + = + +
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(b) 2 ;( 0 ) 1 dy y y dx x == 1 1 2 1 1 sin 1 ln sin 00 0 ln sin x dy dx y x y xC C C yx ye = =+ = = = 3.(24 pts) Classify each sequence as either convergent or divergent. If convergent, find the limit; if divergent, give reasons why. (a) cos 41 n n a n π = + ⎝⎠ Convergent 1 limcos cos lim cos 11 4 2 44 nn n n n ππ →∞ →∞ →∞ ⎛⎞
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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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EXAM3 - Exam 3 solutions Instructions Please show all of...

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