Evaluate $$\lim\limits_{x \to 0}f(x)$$ where $$f(x)=\{\dfrac{x}{|x|},x\neq 0,0,x=0$$

Asked by Pragya Singh | 1 year ago |  213

##### Solution :-

The given function is

$$\lim\limits_{x \to 0^-}f(x)= \lim\limits_{x \to 0^-}[\dfrac{x}{|x|}]$$ 

$$\lim\limits_{x \to 0}(\dfrac{x}{-x})$$

$$\lim\limits_{x \to 0}(-1)$$

= -1

$$\lim\limits_{x \to 0^+}f(x)= \lim\limits_{x \to 0^+}[\dfrac{x}{|x|}]$$

$$\lim\limits_{x \to 0}(\dfrac{x}{x})$$

$$\lim\limits_{x \to 0}(1)$$

It is observed that $$\lim\limits_{x \to 0^-}f(x)\neq\lim\limits_{x \to 0^+}f(x)$$

Hence, $$\lim\limits_{x \to 0}f(x)$$ does not exist

Answered by Pragya Singh | 1 year ago

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