determine the limit shown below in simplest form. lim x→8 (x² - x - 56) / (-2x + 16)
determine the limit shown below in simplest form. lim x→8 (x² - x - 56) / (-2x + 16)
Answer
Explanation:
Step1: Factor the numerator and denominator
The numerator $x^{2}-x - 56=(x - 8)(x+7)$ and the denominator $-2x + 16=-2(x - 8)$. So the function becomes $\lim_{x\rightarrow8}\frac{(x - 8)(x + 7)}{-2(x - 8)}$.
Step2: Simplify the function
Cancel out the common factor $(x - 8)$ (since $x\neq8$ when taking the limit), we get $\lim_{x\rightarrow8}\frac{x + 7}{-2}$.
Step3: Substitute $x = 8$
Substitute $x = 8$ into $\frac{x + 7}{-2}$, we have $\frac{8+7}{-2}=\frac{15}{-2}=-\frac{15}{2}$.
Answer:
$-\frac{15}{2}$