Prove that the \(\lim_{x \to 2} \frac{|x – 2|}{x – 2}\) doesn’t exist.

This answer is restricted. Please login to view the answer of this question.

Login Now

Solution:

We have to evaluate

\(\lim_{x \to 2^{-}} \left ( \frac{|x – 2|}{x – 2} \right )\)

Here,

\(LHL = \lim_{x \to 2^{-}} \left ( \frac{|x – 2|}{x – 2} \right )\)

\(= \lim_{x \to 2^{-}} \left ( \frac{-(x – 2)}{x – 2} \right )\) = -1

and,

\(RHL = \lim_{x \to 2^{+}} \left ( \frac{|x – 2|}{x – 2} \right )\)

\(= \lim_{x \to 2^{-}} \left ( \frac{(x – 2)}{x – 2} \right )\) = 1

This shows LHL ≠ RHL. So, the limit of given function doesn’t exists.

If you found any type of error on the answer then please mention on the comment or report an answer or submit your new answer.
Leave your Answer:

Click here to submit your answer.

Discussion
0 Comments
  Loading . . .