Definition 1. Let ACR and c be a limit point of A. Let f: AR be a function. We say that lim f(x) = ∞ if for all M>0 there exists > 0 I→C so that for all x & A, if 0 < x-c< 6 then f(x) > M. (a) Prove that lim2 = ∞. 2-0 (b) Construct a definition of what "lim f(x) = L" means. Prove that I →∞ lim¹ = 0. 84X (c) What should "lim f(x) = ∞o" mean? Give an example of a function 818 where this holds.
Definition 1. Let ACR and c be a limit point of A. Let f: AR be a function. We say that lim f(x) = ∞ if for all M>0 there exists > 0 I→C so that for all x & A, if 0 < x-c< 6 then f(x) > M. (a) Prove that lim2 = ∞. 2-0 (b) Construct a definition of what "lim f(x) = L" means. Prove that I →∞ lim¹ = 0. 84X (c) What should "lim f(x) = ∞o" mean? Give an example of a function 818 where this holds.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:Definition 1. Let ACR and c be a limit point of A. Let f: A → R be
a function. We say that lim f(x) = ∞ if for all M>0 there exists > 0
I-C
so that for all x & A, if 0 < x-c<d then f(x) > M.
(a) Prove that lim
2-0
= ∞.
(b) Construct a definition of what "lim f(x) = L" means. Prove that
I→∞
lim = 0.
14x
(c) What should " lim f(x) = ∞" mean? Give an example of a function
x →∞
where this holds.
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