Consider the function f(x) = cos¯'. a State the domain of f(x). (Hint: Think about it rather than relying on algebra.) 1 b Recalling that Vx? |x], show that f'(x) = |x|Vx? 1 c Comment on f'(1) andf'(-1).
Consider the function f(x) = cos¯'. a State the domain of f(x). (Hint: Think about it rather than relying on algebra.) 1 b Recalling that Vx? |x], show that f'(x) = |x|Vx? 1 c Comment on f'(1) andf'(-1).
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
![= cos-.
a State the domain of f(x). (Hint: Think about it rather than relying on algebra.)
17 Consider the function f(x)
1
b Recalling that Vx² :
|x], show that f'(x) =
|x|Vx?
- 1
c Comment on f'(1) and f'(-1).
d Use the expression for f'(x) in part b to write down separate expressions for f'(x) when x > 1 and
when x < -1.
e Explain why f(x) is increasing for x > 1 and for x < -1.
f Find:
i lim f(x)
ii
lim f(x)
X- 00
X - 00
g Sketch the graph of y = f(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70beab56-a43b-4c48-9bfa-d1f4d172e84f%2F9f39d14a-def9-4d24-8690-4a8d76ea2588%2F69qgms_processed.jpeg&w=3840&q=75)
Transcribed Image Text:= cos-.
a State the domain of f(x). (Hint: Think about it rather than relying on algebra.)
17 Consider the function f(x)
1
b Recalling that Vx² :
|x], show that f'(x) =
|x|Vx?
- 1
c Comment on f'(1) and f'(-1).
d Use the expression for f'(x) in part b to write down separate expressions for f'(x) when x > 1 and
when x < -1.
e Explain why f(x) is increasing for x > 1 and for x < -1.
f Find:
i lim f(x)
ii
lim f(x)
X- 00
X - 00
g Sketch the graph of y = f(x).
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