Barrons AP Calculus - David Bock
8. (A) ...
BC ONLY (B) Find counterexamples for statements (A), (C), and (D). ...
(D) the general term of a divergent series. ...
(D) (A), (B), (C), and (E) all converge; (D) is the divergent geometric series with r = −1.1. ...
12. (D) ...
(A) If then f (0) is not defined. ...
(C) unless x = 3. ...
(B) The integrated series is See Question 27. ...
16. (E) ...
17. (A) ...
(E) The series satisfies the Alternating Series Test, so the error is less than the first term dropped, namely, (see (5)), in t ...
(D) Note that the Taylor series for tan−1 x satisfies the Alternating Series Test and that then the first omitted term, is nega ...
(E) Now the first omitted term, is positive for x < 0. Hence P 9 (x) is less than tan−1 x. ...
(A) If converges, so does where m is any positive integer; but their sums are probably different. ...
BC ONLY (E) Each series given is essentially a p-series. Only in (E) is p > 1. ...
(C) Use the Integral Test. ...
(C) The limit of the ratio for the series is 1, so this test fails; note for (E) that ...
(B) does not equal 0. ...
(E) Note the following counterexamples: (A) (B) (C) (D) ...
(C) Since the series converges if |x| < 1. We must test the end-points: when x = 1, we get the divergent harmonic series; x ...
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