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(c) h : R → R, h(x) = e". (d) s: (0, ∞) → R, s(x)= ln x. (e) t:R → R, t(x) = sin x.

(c) h : R → R, h(x) = e". (d) s: (0, ∞) → R, s(x)= ln x. (e) t:R → R, t(x) = sin x.

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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c,d,e

 

Use the e – 8 definition of continuity to prove that each of the following functions is continuous on its domain. One key component in each solution is the estimation of the quantity |f(x) – f(c)| using various inequalities and identities. Good luck, analysts! (a) f : R → R, f(x) = |x|. (b) g : (0, 0) → R, g(x) = /x. (c) h: R → R, h(x) = e". (d) s: (0, 0) → R, s(x) = lnx. (e) t: R → R, t(x) = sin x.
Transcribed Image Text:Use the e – 8 definition of continuity to prove that each of the following functions is continuous on its domain. One key component in each solution is the estimation of the quantity |f(x) – f(c)| using various inequalities and identities. Good luck, analysts! (a) f : R → R, f(x) = |x|. (b) g : (0, 0) → R, g(x) = /x. (c) h: R → R, h(x) = e". (d) s: (0, 0) → R, s(x) = lnx. (e) t: R → R, t(x) = sin x.
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