Question

evaluate $lim_{x
ightarrow3}\frac{x^{2}-9}{x - 3}$ if it exists (write
a\) if limit does not exist.

Explanation:

Step1: Factor the numerator

We know that $x^{2}-9=(x + 3)(x - 3)$. So the function becomes $\lim_{x
ightarrow3}\frac{(x + 3)(x - 3)}{x - 3}$.

Step2: Simplify the function

Cancel out the common factor $(x - 3)$ in the numerator and denominator. The function simplifies to $\lim_{x
ightarrow3}(x + 3)$.

Step3: Substitute the value of $x$

Substitute $x = 3$ into $x+3$. We get $3+3=6$.

Answer:

$6$