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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi, can someone help me with this question? Please be specific in the solution
Thanks a lot
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13b2cb16-6e49-4177-a438-0c2d8836d4c6%2Ff60ff295-cf06-4b91-92f8-56d4ab75fc21%2Fjv0bn9v_processed.png&w=3840&q=75)
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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