evaluate the limit, if it exists. (if an answer does not exist, enter dne.)\n lim_{x\rightarrow…
evaluate the limit, if it exists. (if an answer does not exist, enter dne.)\n lim_{x\rightarrow - 5}\frac{x^{2}+5x}{x^{2}-3x - 40}
Answer
Explanation:
Step1: Factor the numerator and denominator
The numerator $x^{2}+5x=x(x + 5)$. The denominator $x^{2}-3x - 40=(x-8)(x + 5)$. So the function becomes $\frac{x(x + 5)}{(x - 8)(x+5)}$.
Step2: Simplify the function
Cancel out the common factor $(x + 5)$ (since $x\neq - 5$ when taking the limit), we get $\lim_{x\rightarrow - 5}\frac{x}{x - 8}$.
Step3: Substitute $x=-5$ into the simplified - function
Substitute $x=-5$ into $\frac{x}{x - 8}$, we have $\frac{-5}{-5-8}=\frac{-5}{-13}=\frac{5}{13}$.
Answer:
$\frac{5}{13}$