If-f-x-x-sin-1-x-where-x-0-then-find-the-value-of-function-at-x-0-and-given-that-function-is-continuous-at-x-0-

Question Number 77533 by vishalbhardwaj last updated on 07/Jan/20

If f (x) = x \sin (\frac{1}{x}) where x \neq 0

then find the value of function at x = 0

and given that function is continuous at x = 0 ?

Answered by MJS last updated on 07/Jan/20

\lim_{x \to 0} x \sin \frac{1}{x} =

[let x = \frac{1}{t}]

= \lim_{t \to \pm \infty} \frac{\sin t}{t} = 0

\Rightarrow f (0) = 0

Commented by vishalbhardwaj last updated on 07/Jan/20

thanks a lot sir