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818 ..) Let f: (0, ∞) → R. Assume that lim f(x) = ∞. Prove that for every sequence (n)-1 such that lim n = ∞, we 818 have lim f(n) = ∞0. 818

818 ..) Let f: (0, ∞) → R. Assume that lim f(x) = ∞. Prove that for every sequence (n)-1 such that lim n = ∞, we 818 have lim f(n) = ∞0. 818

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. (a) 、--. ..) Let f: (0, ∞) → R. Assume that lim f(x) = ∞. Prove that for every sequence (n)-1 such that lim n = ∞, we 818 81x have lim f(n) = ∞0. 84x (b) ) Let pn denote the n'th prime number (e.g., p1 = 2, p2 = 3,...). Compute the following limit lim 318 3p²+Pn (1 + 1) ³0² + P²
Transcribed Image Text:3. (a) 、--. ..) Let f: (0, ∞) → R. Assume that lim f(x) = ∞. Prove that for every sequence (n)-1 such that lim n = ∞, we 818 81x have lim f(n) = ∞0. 84x (b) ) Let pn denote the n'th prime number (e.g., p1 = 2, p2 = 3,...). Compute the following limit lim 318 3p²+Pn (1 + 1) ³0² + P²
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