Exercise 1 Let f(x):= arcsin i) Find the domain of f, its sign, eventual symmetries, limits and eventual asymptotes at the extremes of the domain. ii) Discuss continuity and derivability of f and compute relevant limits for f'. iii) Determine the monotonicity of f and eventual min / max. iv) With all the previous informations, plot a graph of f.

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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Answer (ii), (iii), and (iv) only.
Exercise 1
Let
f(x):= arcsin
|x|
x² + 1
i) Find the domain of f, its sign, eventual symmetries, limits and eventual asymptotes at
the extremes of the domain.
ii) Discuss continuity and derivability of f and compute relevant limits for f'.
iii) Determine the monotonicity of f and eventual min / max.
iv) With all the previous informations, plot a graph of f.
Transcribed Image Text:Answer (ii), (iii), and (iv) only. Exercise 1 Let f(x):= arcsin |x| x² + 1 i) Find the domain of f, its sign, eventual symmetries, limits and eventual asymptotes at the extremes of the domain. ii) Discuss continuity and derivability of f and compute relevant limits for f'. iii) Determine the monotonicity of f and eventual min / max. iv) With all the previous informations, plot a graph of f.
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