evaluate the limit: \n$lim_{x\rightarrow6}\frac{x - 6}{x^{2}-6x}=square$\nenter dne if the limit does not…
evaluate the limit: \n$lim_{x\rightarrow6}\frac{x - 6}{x^{2}-6x}=square$\nenter dne if the limit does not exist.
Answer
Explanation:
Step1: Factor the denominator
Factor $x^{2}-6x$ as $x(x - 6)$. So the limit becomes $\lim_{x\rightarrow6}\frac{x - 6}{x(x - 6)}$.
Step2: Simplify the function
Cancel out the common factor $(x - 6)$ (since $x\neq6$ when taking the limit), we get $\lim_{x\rightarrow6}\frac{1}{x}$.
Step3: Substitute the value of $x$
Substitute $x = 6$ into $\frac{1}{x}$, we have $\frac{1}{6}$.
Answer:
$\frac{1}{6}$