Determine the points in the interval (1, 6) 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. fa) is defined (a is in the domain of f 2. im fix) exists x) is discontinuous at x= (Use a comma to separate answors as needed.) Select the corect choice below and, if necessary, fil in the answer box within your choice. 3. lim f(x)=fa) (the value off equals the limit of fat a). O A. The pointis) at x violate(s) the first condition in the continuity checklist (Use a comma to separate answers as needed.) OB. No points violate the first condition in the continuity checklist. Select the correct choice below and, if necessary, fil in the answer box within 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.) OB. 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 t choice. o correct choice below and, if necessary, fill in the answer box within you O A. The pointis) at x violate(s) the third condition in the continuity checklist. (Use a comma to separate answers as needed.) O B. No points violate the third condition in the continuity checklist.
Determine the points in the interval (1, 6) 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. fa) is defined (a is in the domain of f 2. im fix) exists x) is discontinuous at x= (Use a comma to separate answors as needed.) Select the corect choice below and, if necessary, fil in the answer box within your choice. 3. lim f(x)=fa) (the value off equals the limit of fat a). O A. The pointis) at x violate(s) the first condition in the continuity checklist (Use a comma to separate answers as needed.) OB. No points violate the first condition in the continuity checklist. Select the correct choice below and, if necessary, fil in the answer box within 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.) OB. 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 t choice. o correct choice below and, if necessary, fill in the answer box within you O A. The pointis) at x violate(s) the third condition in the continuity checklist. (Use a comma to separate answers as needed.) O B. No points violate the third condition in the continuity checklist.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 12E
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Transcribed Image Text:Determine the points in the interval (1, 6) 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 =
(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).
A. The point(s) at x =
violate(s) the first condition in the continuity checklist.
Xa
(Use a comma to separate answers as needed.)
Ay
6-
B. No points violate the first condition in the continuity checklist.
Select the correct choice below and, if necessary, fill in the answer box within your choice.
4-
O A. The point(s) at x =
violate(s) the second condition in the continuity checklist.
2-
(Use a comma to separate answers as needed.)
B. No points violate the second condition in the continuity checklist.
0-
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 you
choice.
O A. The point(s) at x =
violate(s) the third condition in the continuity checklist.
(Use a comma to separate answers as needed.)
B. No points violate the third condition in the continuity checklist.
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