Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Can you explain to me how in part C the integral converges
f(x): ~ √(x²+5)³ 3¹ Since 1.+00 11/13 da is convergent, by Asymptotic comparison test the given im- x3 proper integral is convergent. I as x+0. 36) The integrand is continuous in [0, +∞o). Let us study the behaviour of the integrand as a → +∞o: f(x) = x + 0(x) √x+0(x) ~x¹/2. 2017 Politecnico di Torino x + 2 √x+√x+1 By Asymptotic comparison test the improper integral diverges. 3c) The integrand is continuous in its domain (0, +∞o). Therefore, we study the be- haviour of the improper integral at +∞o. 1 1 f(x)= √2x (2x + 1) 2√2x3/2, as x→ +∞0. Since 2 > 1, by Asymptotic comparison test the improper integral converges. 2
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Transcribed Image Text:f(x): ~ √(x²+5)³ 3¹ Since 1.+00 11/13 da is convergent, by Asymptotic comparison test the given im- x3 proper integral is convergent. I as x+0. 36) The integrand is continuous in [0, +∞o). Let us study the behaviour of the integrand as a → +∞o: f(x) = x + 0(x) √x+0(x) ~x¹/2. 2017 Politecnico di Torino x + 2 √x+√x+1 By Asymptotic comparison test the improper integral diverges. 3c) The integrand is continuous in its domain (0, +∞o). Therefore, we study the be- haviour of the improper integral at +∞o. 1 1 f(x)= √2x (2x + 1) 2√2x3/2, as x→ +∞0. Since 2 > 1, by Asymptotic comparison test the improper integral converges. 2
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