Question

Apply L'Hôpital's rule to find the limit:

lim(x → a) [f(x) / g(x)]

A) lim(x → a) [f'(x) / g'(x)]
B) lim(x → a) [f''(x) / g''(x)]
C) lim(x → a) [f(x) / g(x)]
D) lim(x → a) [f'''(x) / g'''(x)]

Answer 1

L'Hôpital's rule is used to find the limit of a fraction when the numerator and denominator both approach zero or infinity. The rule states that if the limit of the ratio of the derivatives of the numerator and denominator exists, then it is equal to the limit of the original fraction.

Step-by-step explanation:

L'Hôpital's rule is used to find the limit of a fraction when the numerator and denominator both approach zero or infinity. The rule states that if the limit of the ratio of the derivatives of the numerator and denominator exists, then it is equal to the limit of the original fraction.

To apply L'Hôpital's rule, take the derivatives of the numerator and denominator separately. Then find the limit of the ratio of the derivatives as x approaches a. This limit will be the same as the limit of the original fraction.

Therefore, the answer is A) lim(x → a) [f'(x) / g'(x)].