lim-x-0-xsin-1-x-

Question Number 100027 by bemath last updated on 24/Jun/20

\lim_{x \to 0} xsin (\frac{1}{x}) ?

Commented by john santu last updated on 24/Jun/20

\lim_{x \to 0} x = 0 & - 1 ⩽ \sin (\frac{1}{x}) ⩽ 1

then \underset{x \to 0}{\lim x} \sin (\frac{1}{x}) = 0

Commented by bobhans last updated on 24/Jun/20

yes correct . \lim = 0

Answered by mathmax by abdo last updated on 24/Jun/20

∣ xsin (\frac{1}{x}) ∣⩽∣ x ∣ \Rightarrow \lim_{x \to 0} xsin (\frac{1}{x}) = 0