lim _{x rightarrow 0} frac{2x}{|x|+x^2} = | vedclass

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(B) To find the limit $\lim _{x \rightarrow 0} \frac{2x}{|x|+x^2}$,we evaluate the Left-Hand Limit $(LHL)$ and Right-Hand Limit $(RHL)$.$LHL = \lim _{

Vedclass · Accepted Answer

Limit does not exist

Vedclass · Answer

(B) To find the limit $\lim _{x ightarrow 0} \frac{2x}{|x|+x^2}$,we evaluate the Left-Hand Limit $(LHL)$ and Right-Hand Limit $(RHL)$.$LHL = \lim _{x ightarrow 0^{-}} \frac{2x}{-x+x^2} = \lim _{x ightarrow 0^{-}} \frac{2}{-1+x} = \frac{2}{-1} = -2$.$RHL = \lim _{x ightarrow 0^{+}} \frac{2x}{x+x^2} = \lim _{x ightarrow 0^{+}} \frac{2}{1+x} = \frac{2}{1} = 2$.Since $LHL 
eq RHL$,the limit does not exist.

$\lim _{x \rightarrow 0} \frac{2x}{|x|+x^2} = $

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