# L'Hospital's Rule

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## Lecture Notes

#### Indeterminate Forms

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Section 1, Page 1

Definition, with explanation that limits leading to indeterminate forms sometimes have values that can be found using calculus. Example of finding the value of a limit that leads to the indeterminate form infinity - infinity.

Instructor: Prof. Jason Starr
Prior Knowledge: Limits (section 2 of lecture 2)

#### L’Hopital’s Rule

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Section 3, Page 3

Method for finding limits that have indeterminate form 0/0. Includes examples.

Instructor: Prof. Jason Starr
Prior Knowledge: Indeterminate Forms (section 1 of this lecture)

#### L’Hopital’s Rule for Other Indeterminate Forms

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Section 4, Page 3 to page 4

Explanation that L'Hopital's rule can be used to find limits that lead to other indeterminate forms as well. Includes examples and proof that L'Hopital's rule applies to limits with indeterminate form infinity/infinity.

Instructor: Prof. Jason Starr
Prior Knowledge: Indeterminate Forms and L'Hopital's Rule (sections 1 and 3 of this lecture)

## Exam Questions

#### L'Hopital's Rule

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Problem 3 (page 1)

Evaluating two limits using L'Hopital's Rule.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### L'Hopital's Rule

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Problem 7.1 (page 5) to problem 7.5 (page 6)

Five questions which involve evaluating limits using L'Hopital's Rule.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Evaluating Limits

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Problem 15 (page 2)

Three limits involving trigonometric, logarithmic, and exponential functions.

Instructor: Prof. David Jerison
Prior Knowledge: None