you do not (a) The domain of f is R. prove or explain your answer, as long (b) lim f(x) does not exist when a € {-2,2,4), and x-a the limit exists for all other a E R. (c) lim f(x) = 0
you do not (a) The domain of f is R. prove or explain your answer, as long (b) lim f(x) does not exist when a € {-2,2,4), and x-a the limit exists for all other a E R. (c) lim f(x) = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Sketch the graph of a function of that satisfies all 10 conditions below simultaneously. For this question,
you do not need to prove or explain your answer, as long as the graph is correct and very clear.
(a) The domain of f is R.
(b) lim f(x) does not exist when a € {-2,2,4}, and
I-a
the limit exists for all other a € R.
(c) lim f(x) = 0
x→0
(d) limf(x)] does not exist
(e) lim f(x) = - ∞
2--2-
7
-6
-5
-4
3
7
2 -1
y
To clarify, we want one single function f that satisfies all the conditions in all the parts, all at once.
Make your graph tidy and unambiguous.
6
5
4
3
2
1
T
-2
-3
-4
-5
(f) lim f(x) = ∞
x-2
-6
(g) lim
(h) lim f(f(x)) = 3
2-4+
m[f(x)]²=
(i) lim f(x) = 2
1418
(j) lim f
x-2
-~
1 2
= 4
¹ (√(12) - 2).
3
= -3
4
5
-co
6
7
x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4893c46-a94c-4c81-a9fc-277ce07300a6%2F9f374727-7497-408f-bdbf-2e9e6e32771e%2Foaiheld_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Sketch the graph of a function of that satisfies all 10 conditions below simultaneously. For this question,
you do not need to prove or explain your answer, as long as the graph is correct and very clear.
(a) The domain of f is R.
(b) lim f(x) does not exist when a € {-2,2,4}, and
I-a
the limit exists for all other a € R.
(c) lim f(x) = 0
x→0
(d) limf(x)] does not exist
(e) lim f(x) = - ∞
2--2-
7
-6
-5
-4
3
7
2 -1
y
To clarify, we want one single function f that satisfies all the conditions in all the parts, all at once.
Make your graph tidy and unambiguous.
6
5
4
3
2
1
T
-2
-3
-4
-5
(f) lim f(x) = ∞
x-2
-6
(g) lim
(h) lim f(f(x)) = 3
2-4+
m[f(x)]²=
(i) lim f(x) = 2
1418
(j) lim f
x-2
-~
1 2
= 4
¹ (√(12) - 2).
3
= -3
4
5
-co
6
7
x
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