using real analysis , Show thatf(x) = x 0 sin(1=x)if if x x 6= 0 = 0is continuous but not differentiable at x = 0 12. Show that(x sin(1/x), if x#0f (x) =10,if x = 0is continuous but not differentiable at x = 0.

The given function is fx=xsin1x, if x≠o0, if x=0. Show that the given function is continuous but not…

Answered: 12. Show that x sin(1/x), if x#0 f(x)=…

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12. Show that x sin(1/x), if x#0 f(x)= 10, if x = 0 is continuous but not differentiable at x = 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

using real analysis , Show that
f(x) =

x 0 sin(1=x)

if if x x 6= 0 = 0

is continuous but not differentiable at x = 0

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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