Problem Statement

{2,4,6,8}
{2,3,4,5}
2*4

Evaluate the limit.

 
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, 2·e4·x - 2 = .

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

Correct.
Incorrect.

Question 2

Thus at x = 0, an indeterminate form, and since both the numerator and denominator differentiable on an open interval containing x = 0, l'Hôpital's Rule apply.

Correct.
Incorrect.

 
Step 2

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

Question 3

Where X = .

Correct.
Incorrect.

 
Step 3

Decide if can be evaluated immediately or if it requires repeating l'Hôpital's Rule by evaluating both the numerator and denominator at x = 0.

Question Sequence

Question 4

At x = 0, 8·ex = .

At x = 0, cos(x) = .

Correct.
Incorrect.

Question 5

Thus, l'Hôpital's Rule apply.

Correct.
Incorrect.

 
Step 4

Question 6

Evaluate the limit.

=

Correct.
Incorrect.