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anskeyevenreview(1)

# anskeyevenreview(1) - a divergent series that doesn’t...

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. MATH 1042 Answer Key to Even Review Problems for Final Exam Spring 2010 Section 5.6 24) e tan θ + C 28) (tan - 1 x ) 3 3 + C 56) tan 5 x 5 + C 60) 2 sin x + C 66) 2 tan x + C Section 5.7 6) ln 2 16) 1 4 arcsin (4 t ) + C Section 6.3 14) 1088 π 15 28) 6 2 2 2 - (2 - y - 2) 2 dy = 40 π 3 Chapter 6 Review Exercises 2) 1 2 Section 7.2 20) 1 3 x 3 ln x - 1 9 x 3 + C 48) 1 4 50) π 4 - ln 2 2 Section 7.3 26) - 1 499 cos 499 y + 1 501 cos 501 y + C 32) sec 5 θ 5 - sec 3 θ 3 + C Section 7.4 10) 1 128 tan - 1 1 4 + 4 17 16) 1 25 x 2 - 5 x + C Section 7.6 30) 2 ln | x - 1 | + 1 2 ln ( x 2 + 1) - 3 tan - 1 x + C Section 7.7 16) 1 2 e 4 44) Diverges 78) π 2 Chapter 7 Review Exercises 40) 2 3 (tan x ) 3 / 2 + C 86) π 2

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Section 10.2 24) S = 1 e - 1 34) Come up with your own counterexamples! (a) The limit of the sequence is not the same at the sum of the series. (b) The N th partial sum is a 1 + a 2 + · · · + a N - 1 + a N (c) The terms tending to zero is necessary for convergence, but not sufficient. (d) The limit of the sequence is not the same at the sum of the series. Section 10.3 12) Converges (Limit Comparison with 1 n 2 ) 18) The second inequality is useful: the first will give that your terms are smaller than terms of
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Unformatted text preview: a divergent series - that doesn’t help you; the second inequality gives the terms are smaller than terms of a convergent series which allows you to conclude convergence. 22) Diverges (Limit Comparison with X 1 √ n ) 34) Converges (Limit Comparison with X 1 n 2 ) 56) Diverges (Test for Divergence) Section 10.4 8) Diverges (Test for Divergence) Section 10.5 42) Converges (Ratio Test) Section 10.6 12) Converges for x in the interval [-2 , 2), diverges otherwise. 40) Substitute-x for x in the series for 1 1-x for 1 1 + x , then integrate that series to get ln (1 + x ). Section 10.7 4) ∞ X n =0 x 4 n +1 6) ∞ X n =0 (-1) n 2 2 n +1 x 2 n +1 (2 n + 1)! 12) ∞ X n =0 x 2 n +2 n ! 50) ∞ X n =0 (-1) n 1 (2 n )!(4 n + 1) 64) e x 3...
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anskeyevenreview(1)

# anskeyevenreview(1) - a divergent series that doesn’t...

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. MATH 1042 Answer Key to Even Review Problems for Final Exam Spring 2010 Section 5.6 24) e tan θ + C 28) (tan - 1 x ) 3 3 + C 56) tan 5 x 5 + C 60) 2 sin x + C 66) 2 tan x + C Section 5.7 6) ln 2 16) 1 4 arcsin (4 t ) + C Section 6.3 14) 1088 π 15 28) 6 2 2 2 - (2 - y - 2) 2 dy = 40 π 3 Chapter 6 Review Exercises 2) 1 2 Section 7.2 20) 1 3 x 3 ln x - 1 9 x 3 + C 48) 1 4 50) π 4 - ln 2 2 Section 7.3 26) - 1 499 cos 499 y + 1 501 cos 501 y + C 32) sec 5 θ 5 - sec 3 θ 3 + C Section 7.4 10) 1 128 tan - 1 1 4 + 4 17 16) 1 25 x 2 - 5 x + C Section 7.6 30) 2 ln | x - 1 | + 1 2 ln ( x 2 + 1) - 3 tan - 1 x + C Section 7.7 16) 1 2 e 4 44) Diverges 78) π 2 Chapter 7 Review Exercises 40) 2 3 (tan x ) 3 / 2 + C 86) π 2

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Section 10.2 24) S = 1 e - 1 34) Come up with your own counterexamples! (a) The limit of the sequence is not the same at the sum of the series. (b) The N th partial sum is a 1 + a 2 + · · · + a N - 1 + a N (c) The terms tending to zero is necessary for convergence, but not sufficient. (d) The limit of the sequence is not the same at the sum of the series. Section 10.3 12) Converges (Limit Comparison with 1 n 2 ) 18) The second inequality is useful: the first will give that your terms are smaller than terms of
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Unformatted text preview: a divergent series - that doesn’t help you; the second inequality gives the terms are smaller than terms of a convergent series which allows you to conclude convergence. 22) Diverges (Limit Comparison with X 1 √ n ) 34) Converges (Limit Comparison with X 1 n 2 ) 56) Diverges (Test for Divergence) Section 10.4 8) Diverges (Test for Divergence) Section 10.5 42) Converges (Ratio Test) Section 10.6 12) Converges for x in the interval [-2 , 2), diverges otherwise. 40) Substitute-x for x in the series for 1 1-x for 1 1 + x , then integrate that series to get ln (1 + x ). Section 10.7 4) ∞ X n =0 x 4 n +1 6) ∞ X n =0 (-1) n 2 2 n +1 x 2 n +1 (2 n + 1)! 12) ∞ X n =0 x 2 n +2 n ! 50) ∞ X n =0 (-1) n 1 (2 n )!(4 n + 1) 64) e x 3...
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The provided text is a list of answers to various mathematical problems, primarily from calculus, including integrals, series, and convergence tests. It does not contain any questions, only the answers or results of the problems.

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