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Unformatted text preview: Math 166 Final Exam Page 5 5. (14 points) Determine whether each inﬁnite series converges or diverges. Indicate the test(s) you use. (a) ∞ X k =1 (1) k 2 k k 2 + 1 (b) ∞ X n =2 ln n n 2 Math 166 Final Exam Page 6 6. (16 points) (a) Find P 2 ( x ), the Taylor polynomial of order 2 based at 1 for f ( x ) = ln x . (b) Bound the error  R 2 ( x )  =  ln xP 2 ( x )  if 1 2 ≤ x ≤ 3 2 . (You my use the formula R n ( x ) = f n +1 ( c ) ( n + 1)! ( xa ) n +1 for some number c between a and x .) Math 166 Final Exam Page 7 7. (14 points) (a) Name the curve with polar equation r = 2 sin θ , and sketch its graph. (b) Set up and evaluate an integral in polar coordinates for the area inside of the graph of part (a)....
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 Spring '08
 Hotlz
 Math, Calculus, Taylor Series, 3k

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