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  • Evaluate each of the following limits Show that 〖lim〗┬(x→4) |x-4|/(x-4) does not exist.

Evaluate each of the following limits

Show that \mathop{\lim }_{x \rightarrow 4}\frac{ \vert x-4 \vert }{x-4} does not exist.

Answers (1)

   \\ \mathop{\lim }_{x \rightarrow 4}\frac{ \vert x-4 \vert }{x-4} \\ \\ LHL=\mathop{\lim }_{x \rightarrow \mathop{4}^{-}}\frac{-x+4}{x-4}=-1 \\ \\ RHL=\mathop{\lim }_{x \rightarrow \mathop{4}^{+}}\frac{x-4}{x-4}=1~ \\ \\ LHL \neq RHL \\ \\

Hence, the limit doesnot exist

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infoexpert21

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