Unformatted text preview: 2 , π, 3 π/ 2 , 2 π .] b) Setup, but DO NOT EVALUATE, integral(s) for the area of the enclosed region. 6) (17 pts) Determine whether each sequence converges or diverges. If it converges, ±nd the limit justifying your steps. If it diverges, explain why. a ) a n = (1) n n 6 n 7 + 30 n 2 b ) a n = ln( n ) 6 + ln(3 n ) c ) a n = (1) n cos(1 /n ) Determine if the following integrals are convergent or divergent. Evaluate those that are convergent. 7) (8 pts) I ∞∞ 4 x 3 ex 4 dx 8) (12 pts) I π/ 2 sec 6 θ dθ [Hint: First separately evaluate the inde±nite integral. If you are unable to do so, at least write the de±nition of how this speci±c improper integral is de±ned.] 9) (5 pts) Determine the FORM of the partial fraction decomposition for x 34 ( x 32 x 2 + x )( x 2 + 4) 3 . DO NOT EVALUATE THE COEFFICIENTS....
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 Fall '08
 Margalat
 Math, Calculus, Derivative, pts, Riemann integral, Tufts University Department of Mathematics

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