Show the _ x 0 1 x does not exist. - Vidyadip

Question

Show the $\lim\limits_{\text{x}\rightarrow0}\frac{1}{\text{x}}$ does not exist.

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Answer

Let $\text{f(x)}=\frac{1}{\text{x}},$ this function is defined for every value of x excepts at x = 0
As $\text{x}\rightarrow0^+,\frac{1}{\text{x}}\rightarrow\infty$
As $\text{x}\rightarrow0^-,\frac{1}{\text{x}}\rightarrow-\infty$
$\therefore\lim\limits_{\text{x}\rightarrow0}\frac{1}{\text{x}}$ does not exist.

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