Evaluate the limit using l'Hôpital's Rule. $\lim _{x \rightarrow 5} \frac{x^{3}-125}{x-5}$
A) 25
B) 0
C) 75
D) 15

Question

Quizplus · Accepted Answer

We can see that when we plug in 5 into the expression, we get an indeterminate form of $\frac{0}{0}$.

Using L'Hôpital's rule, we can take the derivative of the numerator and denominator.

$\lim_{x \rightarrow 5} \frac{x^3-125}{x-5} = \lim_{x \rightarrow 5} \frac{3x^2}{1} = 75$

Therefore, the answer is (C).

Evaluate the Limit Using L'Hôpital's Rule lim⁡x→5x3−125x−5\lim _{x \rightarrow 5} \frac{x^{3}-125}{x-5}limx→5​x−5x3−125​