Get the solution to "Find the following limits or state that they..."

Maiclubk

Answered question

2021-10-15

Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.

lim_{x \to 3} \frac{x - 3}{| x - 3 |}

Nathaniel Kramer

Skilled2021-10-16Added 78 answers

Left hand limit:

lim_{x \to 3^{-}} \frac{x - 3}{| x - 3 |} = lim_{x \to 3^{-}} \frac{x - 3}{- (x - 3)}

= lim_{x \to 3^{-}} (- 1)

= - 1

Right hand limit:

lim_{x \to 3^{+}} \frac{x - 3}{| x - 3 |} = lim_{x \to 3^{+}} \frac{x - 3}{x - 3}

= lim_{x \to 3^{+}} (1)

= 1

Clearly left hand limit and right hand limits are not equal.
Therefore

lim_{x \to 3} \frac{x - 3}{| x - 3 |}

does not exist.

Jeffrey Jordon

Expert2022-07-03Added 2605 answers

Answer is given below (on video)

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