3. Let (0 < x < 1) x; f(x) = { (1 < x < 2) 2x; i) Is the function f(x) continuous on [0, 2]? Explain (a graph is not a proof!) ii) Compute AND graph the function F(æ) = | f(t)dt Hint: Imitate the proof of the problem in the notes/video about the relatioship between integration and differentiation. ii) Is the function F(x) continuous at x = 1?
3. Let (0 < x < 1) x; f(x) = { (1 < x < 2) 2x; i) Is the function f(x) continuous on [0, 2]? Explain (a graph is not a proof!) ii) Compute AND graph the function F(æ) = | f(t)dt Hint: Imitate the proof of the problem in the notes/video about the relatioship between integration and differentiation. ii) Is the function F(x) continuous at x = 1?
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
Help with number 3 please
![3. Let
x;
(0 < x < 1)
f(x) = {
(1<x < 2)
2x;
i) Is the function f(x) continuous on [0, 2]? Explain (a graph is not a proof!)
ii) Compute AND graph the function
F(x) = | f(t)dt
Hint: Imitate the proof of the problem in the notes/video about the relatioship between
integration and differentiation.
ii) Is the function F(x) continuous at x =
1?
iii) Does F'(1) exist? Explain. (Hint: Compute the derivative of F(x) from the left and
right at x =
iv) Does iii) violate the FTC II that states F'(x) = f(x) for all x at which f is continuous?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed14a3ea-da26-4be7-a143-8b845df95e91%2F726547b1-2446-4880-83e4-e09de030e617%2F4cdv4knd_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let
x;
(0 < x < 1)
f(x) = {
(1<x < 2)
2x;
i) Is the function f(x) continuous on [0, 2]? Explain (a graph is not a proof!)
ii) Compute AND graph the function
F(x) = | f(t)dt
Hint: Imitate the proof of the problem in the notes/video about the relatioship between
integration and differentiation.
ii) Is the function F(x) continuous at x =
1?
iii) Does F'(1) exist? Explain. (Hint: Compute the derivative of F(x) from the left and
right at x =
iv) Does iii) violate the FTC II that states F'(x) = f(x) for all x at which f is continuous?
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