AP Calculus BC : Euler's Method and L'Hopital's Rule

Study concepts, example questions & explanations for AP Calculus BC

varsity tutors app store varsity tutors android store

Example Questions

Example Question #485 : Ap Calculus Bc

Evaluate the limit:

Possible Answers:

The limit does not exist

Correct answer:

Explanation:

When evaluating the limit using normal methods (substitution), we get the indeterminate form . When this (or ) occurs, we must use L'Hopital's Rule to evaluate the limit. The rule states that when an indeterminate form results from the limit, 

Taking the derivatives in our limit, we get

The derivatives were found using the following rules:

 , 

Example Question #486 : Ap Calculus Bc

Evaluate the limit

.

Possible Answers:

Correct answer:

Explanation:

Admittedly a more computationally intensive problem, we begin by trying to plug in  into the limit directly, but we get the indeterminate form .

We then apply L'Hôpital's rule and try again:

.

However, plugging in  still yields the indeterminate form , so we are forced to apply L'Hôpital's rule a second time:

.

This time, plugging in  does not produce an indeterminate form, so we may evaluate the limit by setting  as follows:

.

Example Question #487 : Ap Calculus Bc

Evaluate the limit

.

Possible Answers:

Correct answer:

Explanation:

Simply plugging in  into the expression yields the indeterminate form of , so we must resort to using L'Hôpital's rule. We take the derivative of the numerator and denominator, and then look at the limit again.

This time, when we plug in , we do not get an indeterminate form, so we can evaluate the limit by setting :

.

Example Question #488 : Ap Calculus Bc

Possible Answers:

Correct answer:

Explanation:

Example Question #489 : Ap Calculus Bc

Possible Answers:

Correct answer:

Explanation:

Example Question #490 : Ap Calculus Bc

Possible Answers:

Correct answer:

Explanation:

Example Question #491 : Ap Calculus Bc

Possible Answers:

Correct answer:

Explanation:

Example Question #492 : Ap Calculus Bc

Possible Answers:

Correct answer:

Explanation:

Example Question #493 : Ap Calculus Bc

Possible Answers:

Correct answer:

Explanation:

Example Question #494 : Ap Calculus Bc

Possible Answers:

Correct answer:

Explanation:

Learning Tools by Varsity Tutors