1: lim_(x→0) sin((1/x)) 2: lim


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Question Number 58867 by malwaan last updated on 01/May/19

$1 : \underset{x \to 0}{l i m} s i n (\frac{1}{x})$ $2 : \underset{x \to \infty}{l i m} s i n (x)$
Commented by tanmay last updated on 01/May/19

$1) \lim_{x \to 0} s i n (\frac{1}{x})$ $t h e l i m i t i n g v a l u e l i e s b e t w e e n \pm 1$ $2) t = \frac{1}{x} w h e n x \to \infty t \to 0$ $\lim_{t \to 0} s i n (\frac{1}{t})$ $t h e l i m i t i n g v a l u e l i e s b e t w e e n \pm 1$ $a t t a c h i n g g r a p h f o r c l a r i t y .$
Commented by tanmay last updated on 01/May/19

Commented by tanmay last updated on 01/May/19

Commented by malwaan last updated on 01/May/19

$\underset{x \to 0^{+}}{l i m} s i n (\frac{1}{x}) \to + ve$ $\underset{x \to 0^{-}}{l i m} s i n (\frac{1}{x}) \to - ve$ $∴ \underset{x \to 0}{l i m} s i n (\frac{1}{x}) d o e s n o t e x i s t$ $A m I r i g h t ?$ $p l e a s e c h e c k . . . .$
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