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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. x0- A function f whose domain is (-1,1) such that f(x) > 0 for all x E (–1,1), and (ii) lim f(x) = 0. (iii) A function f whose domain is R, such that f is not continuous at 0, but fof is continuous at 0.

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. x0- A function f whose domain is (-1,1) such that f(x) > 0 for all x E (–1,1), and (ii) lim f(x) = 0. (iii) A function f whose domain is R, such that f is not continuous at 0, but fof is continuous at 0.

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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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- A function f whose domain is (-1,1) such that f(x) > 0 for all x E (-1,1), and (ii) lim f(x) = 0. (ii) A function f whose domain is R, such that f is not continuous at 0, but fof is continuous at 0.
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- A function f whose domain is (-1,1) such that f(x) > 0 for all x E (-1,1), and (ii) lim f(x) = 0. (ii) 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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