133exam3xsolution - Math 133 Dr. Kurtz Exam 3 Name_ Section...

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Math 133 Exam 3 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.(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.(12 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 + = + =+ = 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 (1 ) sin 3 n nn a n π + ⎛⎞ = ⎜⎟ ⎝⎠ Since 2 ) ) 1 1 33 3 n n 3 ππ ++ == + , it follows that 2 ) 3 sin sin n + →= 2 , so the sequence is convergent.
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133exam3xsolution - Math 133 Dr. Kurtz Exam 3 Name_ Section...

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