Barrons AP Calculus - David Bock
(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 ...
(A) for all x ≠ −1; since the given series converges to 0 if x = −1, it therefore converges for all x. ...
(B) The differentiated series is ...
(B) See Example 52. ...
(D) Note that every derivative of ex is e at x = 1. The Taylor series is in powers of (x − 1) with coefficients of the form ...
(D) For f (x) = cos x around ...
(C) Note that ln q is defined only if q > 0, and that the derivatives must exist at x = a in the formula for the Taylor seri ...
(A) Use Or use the series for ex and let x = −0.1. ...
BC ONLY 35. (C) Or generate the Maclaurin series for esin x. ...
(E) (A), (B), (C), and (D) are all true statements. ...
37. (A) ...
38. (C) Since the series converges when that is, when the radius of convergence is ...
(E) The Maclaurin series sin x = converges by the Alternating Series Test, so the error |R 4 | is less than the first omitted t ...
40. (D) ...
BC ONLY (C) f (x) = a 0 + a 1 x + a 2 x^2 + a 3 x^3 + · · · ; if f (0) = 1, then a 0 = 1. f′ (x) = a 1 + 2a 2 x + 3a 3 x^2 + 4 ...
(D) Use a calculator to verify that the ratio (of the given geometric series) equals approximately 0.98. Since the ratio r < ...
(A) Since the given series converges by the Alternating Series Test, the error is less in absolute value than the first term dr ...
(C) This polynomial is associated with the binomial series (1 + x)p. Verify that f (0) = 1, f ′(0) = p, f ′′(0) = p(p − 1), f′′ ...
(A) The fastest way to find the series for ln(1 + 2x) about x = 0 is to substitute 2x for x in the series ...
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