Question

question 8
evaluate the following limit:
\\(\lim\limits_{x\to 4} \frac{x^2 - 16}{x - 4}\\)
\\(\bigcirc\\) undefined
\\(\bigcirc\\) infinity
\\(\bigcirc\\) -8
\\(\bigcirc\\) 8
\\(\bigcirc\\) -1/8
\\(\bigcirc\\) 0
\\(\bigcirc\\) -infinity

Explanation:

Step1: Factor numerator

The numerator $x^2-16$ is a difference of squares, so it factors to $(x-4)(x+4)$.
$\lim_{x \to 4} \frac{(x-4)(x+4)}{x-4}$

Step2: Cancel common factors

Cancel the $(x-4)$ term from numerator and denominator (valid since $x
eq 4$ when taking the limit).
$\lim_{x \to 4} (x+4)$

Step3: Substitute $x=4$

Replace $x$ with 4 in the simplified expression.
$4+4=8$

Answer:

8 (corresponding to the option: 8)