Problem Statement

{2,4,6,8}
3*4
6*4

Use l'Hôpital's Rule to evaluate the limit or state that l'Hôpital's Rule does not apply.

 
Step 1

L'Hôpital's Rule states that for functions f(x) and g(x) that are differentiable on an open interval containing x = a, and if f(a) = g(a) = 0, then

if the limit on the right exists or is infinite.

Question Sequence

Question 1

To determine whether l'Hôpital's Rule applies to the given problem, evaluate both the numerator and denominator at x = 0.

At x = 0, 4·x3 = .

At x = 0, sin(x) - x = .

Correct.
Incorrect.

 
Step 2

In order to apply l'Hôpital's Rule on the given limit, determine the derivatives of the numerator and denomintor.

Question 3

4·x3 =·x2

sin(x) - x = - 1

Correct.
Incorrect.

 
Step 3

Apply l'Hôpital's Rule on the given limit.

 
Step 4

To determine whether l'Hôpital's Rule applies to , follow the same procedure as in Step 1 by evaluating both the numerator and denominator at x = 0.

Question Sequence

Question 4

At x = 0, 12·x2 = .

At x = 0, cos(x) - 1 = .

Correct.
Incorrect.

 
Step 5

Question 6

In order to apply l'Hôpital's Rule a second time, determine the derivatives of the numerator and denominator.

12·x2 = ·x

cos(x) - 1 =

Correct.
Incorrect.