Evaluate the following limits. Show that _ x 4 |x+4| x-4 does not… - Vidyadip

Question

Evaluate the following limits.
Show that $\lim\limits_{\text{x} \rightarrow 4}\frac{|\text{x}+4|}{\text{x}-4}$ does not exists.

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Answer

Given $\lim\limits_{\text{x} \rightarrow 4}\frac{|\text{x}+4|}{\text{x}-4}$
$\text{L}.\text{H}.\text{L}=\lim\limits_{\text{x} \rightarrow 4}\frac{-(\text{x}+4)}{\text{x}-4}=-1$
$\text{R}.\text{H}.\text{L}=\lim\limits_{\text{x} \rightarrow 4}\frac{\text{x}-4}{\text{x}-4}=1$
Since $\text{L}.\text{H}.\text{L}\neq\text{R}.\text{H}.\text{L}$
Hence, the limit does not exist.

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