Determine the points in the interval (0, 5) at which the function has discontinuities. For each point state the conditions in the continuity checklist that are violated. In order for f to be continuous at a, the following three conditions must hold. 1. f(a) is defined (a is in the domain of f). 2. lim f(x) exists. f(x) is discontinuous at x = 2,3 (Use a comma to separate answers as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice. Xa 3. lim f(x) = f(a) (the value of f equals the limit of f at a). O A. The point(s) at x = 2 violate(s) the first condition in the continuity Xa checklist. Ay 6- (Use a comma to separate answers as needed.) O B. No points violate the first condition in the continuity checklist. 4- Select the correct choice below and, if necessary, fill in the answer box within your choice. 2- O A. The point(s) at x = 3 violate(s) the second condition in the continuity checklist. (Use a comma to separate answers as needed.) O B. No points violate the second condition in the continuity checklist. Note that the third condition is automatically violated if either the first or the second condition is violated. Select the e in the answer box within your choice. choice below if necessary, fill O A. The point(s) at x = 2,3 violate(s) the third condition in the continuity checklist. (Use a comma to separate answers as needed.)
Determine the points in the interval (0, 5) at which the function has discontinuities. For each point state the conditions in the continuity checklist that are violated. In order for f to be continuous at a, the following three conditions must hold. 1. f(a) is defined (a is in the domain of f). 2. lim f(x) exists. f(x) is discontinuous at x = 2,3 (Use a comma to separate answers as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice. Xa 3. lim f(x) = f(a) (the value of f equals the limit of f at a). O A. The point(s) at x = 2 violate(s) the first condition in the continuity Xa checklist. Ay 6- (Use a comma to separate answers as needed.) O B. No points violate the first condition in the continuity checklist. 4- Select the correct choice below and, if necessary, fill in the answer box within your choice. 2- O A. The point(s) at x = 3 violate(s) the second condition in the continuity checklist. (Use a comma to separate answers as needed.) O B. No points violate the second condition in the continuity checklist. Note that the third condition is automatically violated if either the first or the second condition is violated. Select the e in the answer box within your choice. choice below if necessary, fill O A. The point(s) at x = 2,3 violate(s) the third condition in the continuity checklist. (Use a comma to separate answers as needed.)
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:Determine the points in the interval (0, 5) at which the function has discontinuities.
For each point state the conditions in the continuity checklist that are violated. In
order for f to be continuous at a, the following three conditions must hold.
f(x) is discontinuous at x = 2,3
(Use a comma to separate answers as needed.)
1. f(a) is defined (a is in the domain of f).
2. lim f(x) exists.
Select the correct choice below and, if necessary, fill in the answer box within your
choice.
Xa
3. lim f(x) = f(a) (the value of f equals the limit of f at a).
A. The point(s) at x = 2 violate(s) the first condition in the continuity
Xa
checklist.
Ay
6-
(Use a comma to separate answers as needed.)
B. No points violate the first condition in the continuity checklist.
4-
Select the correct choice below and, if necessary, fill in the answer box within your
choice.
2-
O A. The point(s) at x = 3 violate(s) the second condition in the continuity
checklist.
0-
(Use a comma to separate answers as needed.)
4
6
B. No points violate the second condition in the continuity checklist.
Note that the third condition is automatically violated if either the first or the
second condition is violated. Select the correct choice below and, if necessary, fill
in the answer box within your choice.
A. The point(s) at x= 2,3 violate(s) the third condition in the continuity
checklist.
(Use a comma to separate answers as needed.)
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