Question

Evaluate the following limit using L'Hôpital's Rule:

limx→012xe 9 x−6x.
A) 9
B) 12
C) 6
D) 0

Answer 1

To evaluate the given limit using L'Hôpital's Rule, differentiate the numerator and denominator, and then take the limit as x approaches 0. The answer is 0.

Step-by-step explanation:

To evaluate the given limit using L'Hôpital's Rule, we can first rewrite the expression as

lim x→0 (12x - 6x) / (x^9)

Next, we can differentiate the numerator and denominator with respect to x. The derivative of 12x - 6x is 12 - 6 = 6, and the derivative of x^9 is 9x^8.

Taking the limit as x approaches 0, we get

lim x→0 6 / (9x^8)

Since the limit of a constant divided by x^8 as x approaches 0 is 0, the answer is D) 0.