determine-the-interval-on-which-the-given-function-is-continuous-f-x-sin-1-x-x-0-x-x-0-

Question Number 25846 by rita1608 last updated on 15/Dec/17

d e t e r m i n e t h e i n t e r v a l o n w h i c h t h e

g i v e n f u n c t i o n i s c o n t i n u o u s

f (x) = {\begin{cases} \sin \frac{1}{x} & x \neq 0 \\ x & x = 0 \end{cases}

Commented by kaivan.ahmadi last updated on 15/Dec/17

since li \underset{x \to 0}{m s i n} \frac{1}{x} \neq f (0), f (x) is not continuous .

this limit is not exixst .

so the interval is R - {0}

Commented by prakash jain last updated on 16/Dec/17

Commented by kaivan.ahmadi last updated on 17/Dec/17

in definition we must have

∣ \sin (\frac{1}{x}) - A ∣< ϵ .

why \sin \frac{1}{x} ⩾ ϵ ?