Find the limit, if it exists.
-$$\lim _ { x \rightarrow 8 } \frac { x ^ { 2 } + 2 x - 80 } { x ^ { 2 } - 64 }$$
A) $\frac { 9 } { 8 }$
B) $- \frac { 1 } { 8 }$
C) 0
D) Does not exist

Question

Quizplus · Accepted Answer

The limit can be found by simplifying the expression. Factor both the numerator and the denominator: $$\frac{x^2 + 2x - 80}{x^2 - 64} = \frac{(x + 10)(x - 8)}{(x + 8)(x - 8)}$$. Canceling the common factor $(x - 8)$, we get $\frac{x + 10}{x + 8}$. Substituting $x = 8$, we get $\frac{8 + 10}{8 + 8} = \frac{18}{16} = \frac{9}{8}$.

Find the Limit, If It Exists lim⁡x→8x2+2x−80x2−64\lim _ { x \rightarrow 8 } \frac { x ^ { 2 } + 2 x - 80 } { x ^ { 2 } - 64 }x→8lim​x2−64x2+2x−80​

Find the Limit, If It Exists $\lim _ { x \rightarrow 8 } \frac { x ^ { 2 } + 2 x - 80 } { x ^ { 2 } - 64 }$