Find the limit, if it exists.
-$$\lim _ { x \rightarrow 5 } \frac { x ^ { 2 } - 25 } { x ^ { 2 } - 9 x + 20 }$$
A) Does not exist
B) 0
C) 5
D) 10

Question

Quizplus · Accepted Answer

The given limit can be simplified by factoring both the numerator and the denominator. The numerator $x^2 - 25$ factors into $(x + 5)(x - 5)$, and the denominator $x^2 - 9x + 20$ factors into $(x - 5)(x - 4)$. Thus, the expression simplifies to $\frac{(x + 5)(x - 5)}{(x - 5)(x - 4)}$. Canceling the $(x - 5)$ terms, we get $\frac{x + 5}{x - 4}$. Substituting $x = 5$ into the simplified expression gives $\frac{5 + 5}{5 - 4} = \frac{10}{1} = 10$. Therefore, the limit exists and is equal to 10.

Find the Limit, If It Exists lim⁡x→5x2−25x2−9x+20\lim _ { x \rightarrow 5 } \frac { x ^ { 2 } - 25 } { x ^ { 2 } - 9 x + 20 }x→5lim​x2−9x+20x2−25​

Find the Limit, If It Exists $\lim _ { x \rightarrow 5 } \frac { x ^ { 2 } - 25 } { x ^ { 2 } - 9 x + 20 }$