133exam3bsolution - Exam 3 solutions Instructions: Please...

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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) Setting gives 2 1 u =+ x 2 2 1 1 22 2 2 00 1 1 11 1 1 1 lim lim lim lim 1 (1 ) ) 2 2 2 1 2 t tt t t xdx xdx du xx u u t + ∞+ →∞ →∞ ⎛⎞ = = =−=− + = ⎜⎟ ++ + ⎝⎠ ∫∫ 1 (b) 1 0 1 lim lim 2 1 lim 2 1 2 2 t t t dx dx xt −− →→ ⎡⎤ == = + ⎣⎦ = 2.(10 pts) Solve the initial value problem. Write y explicitly as a function of x . 2 2 1 1 1 1 ;( 1 ) 1 tan ln tan 1 ln1 4 tan ln 4 tan ln 4 dy y y dx x dy dx yx C C C π + = + = 1
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3.(24 pts) Classify each sequence as either convergent or divergent. If convergent, find the limit; if divergent, give reasons why. (a) 2 2 2 ln 1 n n a n ⎛⎞ = + ⎝⎠ Convergent. 2 2 2 22 lim lim 2 1 1 1 nn n n n →∞ →∞ == + + , so 2 2 2 lim ln ln 2 1 n n n →∞ = ⎜⎟ + (b) 1 sin n an n = Convergent.
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This note was uploaded on 02/05/2010 for the course MATH 133 taught by Professor Wei during the Fall '07 term at Michigan State University.

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133exam3bsolution - Exam 3 solutions Instructions: Please...

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