Determine the points on the interval (1,5) at which the function f has a discontinuity. At each point of discontinuity state the conditions in the continuity checklist that are violated. 1. f(a) is defined (a is in the domain of f). 2. lim f(x) exists. x-a 3. lim f(x) = f(a) (the value of f equals the limit of f at a). x-a y ☑ 3- y = f(x) 3 6 x Q Q f(x) is discontinuous at x= 2,3,4 (Use a comma to separate answers as needed.) Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The point(s) at x= violate(s) the first condition in the continuity checklist. (Use a comma to separate answers as needed.) B. No point violates the first condition in the continuity checklist. Select the correct choice and, if necessary, fill in the answer box to complete your choice. OA. The point(s) at x= violate(s) the second condition in the continuity checklist. (Use a comma to separate answers as needed.) B. No point violates the second condition in the continuity checklist. The third condition is only considered when the first and second conditions are satisfied. Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. The point(s) at x= | satisfies/satisfy the first and second conditions, but violate(s) the third condition in the continuity checklist. (Use a comma to separate answers as needed.) B. No point violates the third condition in the continuity checklist while satisfying the first and second conditions.
Determine the points on the interval (1,5) at which the function f has a discontinuity. At each point of discontinuity state the conditions in the continuity checklist that are violated. 1. f(a) is defined (a is in the domain of f). 2. lim f(x) exists. x-a 3. lim f(x) = f(a) (the value of f equals the limit of f at a). x-a y ☑ 3- y = f(x) 3 6 x Q Q f(x) is discontinuous at x= 2,3,4 (Use a comma to separate answers as needed.) Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The point(s) at x= violate(s) the first condition in the continuity checklist. (Use a comma to separate answers as needed.) B. No point violates the first condition in the continuity checklist. Select the correct choice and, if necessary, fill in the answer box to complete your choice. OA. The point(s) at x= violate(s) the second condition in the continuity checklist. (Use a comma to separate answers as needed.) B. No point violates the second condition in the continuity checklist. The third condition is only considered when the first and second conditions are satisfied. Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. The point(s) at x= | satisfies/satisfy the first and second conditions, but violate(s) the third condition in the continuity checklist. (Use a comma to separate answers as needed.) B. No point violates the third condition in the continuity checklist while satisfying the first and second conditions.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Determine the points on the interval (1,5) at which the function f has a
discontinuity. At each point of discontinuity state the conditions in the
continuity checklist that are violated.
1. f(a) is defined (a is in the domain of f).
2. lim f(x) exists.
x-a
3. lim f(x) = f(a) (the value of f equals the limit of f at a).
x-a
y
☑
3-
y = f(x)
3
6
x
Q
Q
f(x) is discontinuous at x= 2,3,4
(Use a comma to separate answers as needed.)
Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A. The point(s) at x=
violate(s) the first condition in the continuity checklist.
(Use a comma to separate answers as needed.)
B. No point violates the first condition in the continuity checklist.
Select the correct choice and, if necessary, fill in the answer box to complete your choice.
OA. The point(s) at x=
violate(s) the second condition in the continuity checklist.
(Use a comma to separate answers as needed.)
B. No point violates the second condition in the continuity checklist.
The third condition is only considered when the first and second conditions are satisfied. Select the correct choice and,
if necessary, fill in the answer box to complete your choice.
O A. The point(s) at x= | satisfies/satisfy the first and second conditions, but violate(s) the third condition in the
continuity checklist.
(Use a comma to separate answers as needed.)
B. No point violates the third condition in the continuity checklist while satisfying the first and second conditions.
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