Question

1. \\( \lim _ { x \

ightarrow 4 } \frac { x - 4 } { x ^ { 2 } - 16 } \\)

Explanation:

Step1: Factor the denominator

$$x^2 - 16=(x - 4)(x + 4)$$
So the limit becomes $\lim_{x
ightarrow4}\frac{x - 4}{(x - 4)(x + 4)}$

Step2: Simplify the expression

Cancel out the common factor $(x - 4)$ (for $x
eq4$). The expression simplifies to $\lim_{x
ightarrow4}\frac{1}{x + 4}$

Step3: Substitute $x = 4$

Substitute $x = 4$ into $\frac{1}{x + 4}$. We get $\frac{1}{4+4}=\frac{1}{8}$

Answer:

$\frac{1}{8}$