Question-98544

Question Number 98544 by abony1303 last updated on 14/Jun/20

Commented by abony1303 last updated on 14/Jun/20

Pls help

Answered by mathmax by abdo last updated on 14/Jun/20

\lim_{x \to 0} \frac{f (x) - f (0)}{x - 0} = \lim_{x \to 0} \frac{x^{2} \sin (\frac{1}{x}) + 0}{x} = \lim_{x \to 0} xsin (\frac{1}{x}) = 0

because ∣ xsin (\frac{1}{x}) ∣ ⩽∣ x ∣ \Rightarrow f is derivable at 0 and f^{^{'}} (0) = 0