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 - 1}\frac{x^{2}-6x}{x^{2}-5x - 6}
Answer
Explanation:
Step1: Factor the numerator and denominator
The numerator $x^{2}-6x=x(x - 6)$. The denominator $x^{2}-5x - 6=(x + 1)(x-6)$. So the function becomes $\frac{x(x - 6)}{(x + 1)(x - 6)}$.
Step2: Simplify the function
Cancel out the common factor $(x - 6)$ (for $x\neq6$). The simplified function is $\frac{x}{x + 1}$.
Step3: Substitute the limit value
Substitute $x=-1$ into $\frac{x}{x + 1}$. We get $\frac{-1}{-1+1}=\frac{-1}{0}$, which is undefined.
Answer:
DNE