n each part below, give an example of a function which satisfies the given criteria. Justify that your xample is correct. You should give the simplest example of which you can think. (i) A function f whose domain is (–1,1) such that lim f(x) = 3 and lim f(x) = -2. T→0+ x→0- ii) lim f(x) = 0. A function f whose domain is (-1,1) such that f(x) > 0 for all x e (-1, 1), and ii) A function f whose domain is R, such that f is not continuous at 0, but fof is continuous at 0.
n each part below, give an example of a function which satisfies the given criteria. Justify that your xample is correct. You should give the simplest example of which you can think. (i) A function f whose domain is (–1,1) such that lim f(x) = 3 and lim f(x) = -2. T→0+ x→0- ii) lim f(x) = 0. A function f whose domain is (-1,1) such that f(x) > 0 for all x e (-1, 1), and ii) A function f whose domain is R, such that f is not continuous at 0, but fof is continuous at 0.
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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Transcribed Image Text:4. In each part below, give an example of a function which satisfies the given criteria. Justify that your
example is correct. You should give the simplest example of which you can think.
(i)
A function f whose domain is (-1,1) such that lim f(x) = 3 and lim f(x) =
= -2.
x→0+
x→0-
(ii)
lim f(x) = 0.
A function f whose domain is (-1,1) such that f(x) > 0 for all x e (-1, 1), and
x→0
(iii)
A function f whose domain is R, such that f is not continuous at 0, but fof is continuous
at 0.
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