Question

find the given limit.
\\(\lim\limits_{x\to 12^+} \sqrt{x^2 - 144}\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice

\\(\bigcirc\\) a. \\(\lim\limits_{x\to 12^+} \sqrt{x^2 - 144} = \square\\)
\\(\bigcirc\\) b. the limit does not exist and is not \\(\infty\\) or \\(-\infty\\)

Explanation:

Step1: Substitute x=12 into the expression

$\sqrt{12^2 - 144} = \sqrt{144 - 144} = \sqrt{0} = 0$

Step2: Check right-hand limit behavior

As $x \to 12^+$, $x^2 - 144$ approaches 0 from the positive side, so its square root approaches 0.

Answer:

A. $\lim_{x \to 12^+} \sqrt{x^2 - 144} = 0$