evaluate $lim_{x\rightarrow3}\frac{x^{2}-9}{x - 3}$ if it exists (write \na\) if limit does not exist.
evaluate $lim_{x\rightarrow3}\frac{x^{2}-9}{x - 3}$ if it exists (write \na\) if limit does not exist.
Answer
Explanation:
Step1: Factor the numerator
We know that $x^{2}-9=(x + 3)(x - 3)$. So the function becomes $\lim_{x\rightarrow3}\frac{(x + 3)(x - 3)}{x - 3}$.
Step2: Simplify the function
Cancel out the common factor $(x - 3)$ in the numerator and denominator. The function simplifies to $\lim_{x\rightarrow3}(x + 3)$.
Step3: Substitute the value of $x$
Substitute $x = 3$ into $x+3$. We get $3+3=6$.
Answer:
$6$