The value of lim _{x rightarrow 0} frac{x}{|x | vedclass

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(D) To find the limit,we evaluate the left-hand limit $(L.H.L.)$ and the right-hand limit $(R.H.L.)$ at $x = 0$.$L.H.L. = \lim _{x \rightarrow 0^{-}}

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does not exist.

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(D) To find the limit,we evaluate the left-hand limit $(L.H.L.)$ and the right-hand limit $(R.H.L.)$ at $x = 0$.$L.H.L. = \lim _{x ightarrow 0^{-}} \frac{x}{|x|+x^2} = \lim _{x ightarrow 0^{-}} \frac{x}{-x+x^2} = \lim _{x ightarrow 0^{-}} \frac{1}{-1+x} = \frac{1}{-1} = -1$.$R.H.L. = \lim _{x ightarrow 0^{+}} \frac{x}{|x|+x^2} = \lim _{x ightarrow 0^{+}} \frac{x}{x+x^2} = \lim _{x ightarrow 0^{+}} \frac{1}{1+x} = \frac{1}{1} = 1$.Since $L.H.L. 
eq R.H.L.$,the limit does not exist.

The value of $\lim _{x \rightarrow 0} \frac{x}{|x|+x^2}$ is .

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