**Unformatted text preview: **09/28/2000 THU 09:27 FAX 6434330 MOFFITT LIBRARY .001 Second Midterm Examw—GO points
1 (5 points each). Find the sums of the following series: 00 n+1 n+2
a. ”2—1[ln( n )—ln(n+l):|. b-:(s<z>"—4<—:>”“)- 2 {7' points each}. Determine Whether each series is divergent, conditionally convergent,
or absolutely convergent: 00 n 1 (n + l)! _ n!
.a. :jéf—l) + m 00 1)n+1 71’ l
b.2—1ni3tan(4+n). 3
H 3 ( 5 points each). Decide Whether the following inﬁnite series converge or diverge: 20103;) SH” 4a (6 points}. Consider the curve with polar equation 7" : 1 + 2 cos(6). Express in terms
of deﬁnite integrals the area inside the small loop. [The problem was accompanied by a small graph of the curve, produced by Mathematica] 4b (6 points). Find the slope of the line tangent to the polar curve 7“ = 1 + 2 c0509) at the
point with 9 = 7r/2. 5a {5 points ) Express in terms of deﬁnite integrals the length of the entire curve
7" = l + 2cos(6) (both loops). . What function [\DII—I 5b (7 points). Suppose that f(.’L' —; ans-n for all 1' such that |;1:| 3
:0 DC
has Taylor series E nzanasn'!’ n=2 ...

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