Problem 4.1.5 Define f: RR by 0:={8 if z € Q. otherwise. Prove that f is differentiable at 0 but discontinuous at all other points. f(x):= Problem 4.1.6 Assume the inequality - sinz ². Prove that sin is differentiable at 0 and find the derivative at 0. Problem 4.1.7 Using the previous exercise, prove that sin is differentiable at all x and that the derivative is cosx. (Hint: Use the sum-to-product trigonometric identity.)
Problem 4.1.5 Define f: RR by 0:={8 if z € Q. otherwise. Prove that f is differentiable at 0 but discontinuous at all other points. f(x):= Problem 4.1.6 Assume the inequality - sinz ². Prove that sin is differentiable at 0 and find the derivative at 0. Problem 4.1.7 Using the previous exercise, prove that sin is differentiable at all x and that the derivative is cosx. (Hint: Use the sum-to-product trigonometric identity.)
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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Transcribed Image Text:Problem 4.1.5
Define f: RR by
if z € Q.
otherwise.
Prove that f is differentiable at 0 but discontinuous at all other points.
0:={8
f(x):=
Problem 4.1.6
Assume the inequality - sinz ². Prove that sin is differentiable at 0 and find the derivative at
0.
Problem 4.1.7
Using the previous exercise, prove that sin is differentiable at all x and that the derivative is cosx.
(Hint: Use the sum-to-product trigonometric identity.)
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