question 13 evaluate the limit $lim_{x\rightarrow - 9}\frac{x^{2}+16x + 63}{x + 9}$

question 13 evaluate the limit $lim_{x\rightarrow - 9}\frac{x^{2}+16x + 63}{x + 9}$

question 13 evaluate the limit $lim_{x\rightarrow - 9}\frac{x^{2}+16x + 63}{x + 9}$

Answer

Explanation:

Step1: Factor the numerator

We factor (x^{2}+16x + 63) as ((x + 7)(x+9)). So the limit becomes (\lim_{x\rightarrow - 9}\frac{(x + 7)(x + 9)}{x+9}).

Step2: Cancel out common factors

Since (x\neq - 9) when taking the limit (we are approaching - 9), we can cancel out the ((x + 9)) terms. The expression simplifies to (\lim_{x\rightarrow - 9}(x + 7)).

Step3: Substitute the value of x

Substitute (x=-9) into (x + 7). We get (-9+7=-2).

Answer:

(-2)