26) Consider the function S1 if 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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Solve both 26 and 27 please
![26) Consider the function
f(x) = {
1 if 0 <x < 1,
x if x E [1,2].
Let F(x) = So f(t)dt for each x E [0, 2].
Which of the following statements are true?
a) F(x) = x for all x E [0, 1].
b) F(x) = for all x E [1,2]
c) F is discontinuous at x = 1.
d) F is continuous at x = 1 but not differentiable.
e) F is differentiable at = 1 and F'(1) = 1.
27) Assume that f is continuous and strictly increasing on [0, 1] with f(0) = 0 and
f(1) = 2. Assume that g is the inverse of f over (0, 1]. Assume that f(t)dt = .
Which of the following statements are true?
a) So 9(t)dt
= }.
1
b) g(t)dt = .
4
3*
c) So f(t) + g(t) dt = 2.
d) So f(t)dt = 6 1 – g(t)dt.
e) f 9(t)dt = f, 2 – f(t)dt.
|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09caa562-c0c8-4a11-85df-abb5e549e1a9%2F00fa14e6-cc1b-46d9-b4da-b55586e2ceee%2Fwlh8v1n_processed.png&w=3840&q=75)
Transcribed Image Text:26) Consider the function
f(x) = {
1 if 0 <x < 1,
x if x E [1,2].
Let F(x) = So f(t)dt for each x E [0, 2].
Which of the following statements are true?
a) F(x) = x for all x E [0, 1].
b) F(x) = for all x E [1,2]
c) F is discontinuous at x = 1.
d) F is continuous at x = 1 but not differentiable.
e) F is differentiable at = 1 and F'(1) = 1.
27) Assume that f is continuous and strictly increasing on [0, 1] with f(0) = 0 and
f(1) = 2. Assume that g is the inverse of f over (0, 1]. Assume that f(t)dt = .
Which of the following statements are true?
a) So 9(t)dt
= }.
1
b) g(t)dt = .
4
3*
c) So f(t) + g(t) dt = 2.
d) So f(t)dt = 6 1 – g(t)dt.
e) f 9(t)dt = f, 2 – f(t)dt.
|
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