Limx #8594;0sinxxL.H.Llimx #8594;0 sinxxi.e. #160;limx #8594;0 sinxxi.e. #160; limx #8594;0sinxx= 1i.e. #160;left #160;hand #160;limit #160; ...

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Factorization Method Form to Remove Indeterminate Form

lim x → 0 sin...

Question

$\lim_{x \to 0} \frac{|\sin x|}{x}________________________________.$

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Solution

$\begin{matrix} \lim \\ x \to 0 \end{matrix} \frac{|\sin x|}{x} L . H . L \begin{matrix} \lim \\ x \to 0^{-} \end{matrix} \frac{|\sin x|}{x} i . e . \begin{matrix} \lim \\ x \to 0 \end{matrix} \frac{- \sin x}{x} i . e . \begin{matrix} - \lim \\ x \to 0 \end{matrix} \frac{\sin x}{x} = - 1 i . e . left hand limit is - 1 R . H . L \begin{matrix} \lim \\ x \to 0^{+} \end{matrix} \frac{|\sin x|}{x} i . e . \begin{matrix} \lim \\ x \to 0 \end{matrix} \frac{\sin x}{x} i . e . R . H . L = 1 Since L . H . L \neq R . H . S Hence, \begin{matrix} \lim \\ x \to 0 \end{matrix} \frac{|\sin x|}{x} does not exist$

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