3. Let {: (0
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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Question
Just the last two parts. Thanks. (iii, iv).
![3. Let
(0 <x < 1)
(1 < x < 2)
f(x) =
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?
iii) Does F'(1) exist? Explain. (Hint: Compute the derivative of F(x) from the left and
right at x = 1
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%2Ffbb66fa7-7c22-4982-a22f-aaed542f65b3%2Fa2ed77db-8021-45ed-bb77-d2315d8b2ef9%2Fpqoowff_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let
(0 <x < 1)
(1 < x < 2)
f(x) =
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?
iii) Does F'(1) exist? Explain. (Hint: Compute the derivative of F(x) from the left and
right at x = 1
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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