ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

4.7 Using L'Hopitals Rule for Determining Limits in Indeterminate Forms

#l'hopitals

#limits

โฑ๏ธย ย 1 min read

written by

Meghan Dwyer

meghan dwyer

June 22, 2020


Indeterminate Forms

Remember those times when you were solving limits at infinity, and you would come out with an answer that looked like โ™พ๏ธ/โ™พ๏ธ or 0/0, and you would have to see if there was another way to manipulate the equation or cancel out some terms to try and find an answer that was not in an indeterminate form?

Well, no more of that! Now that you know what derivatives are, we can use those!

L'Hopital's Rule

If you are solving a limit, and you end up with an answer in the form โ™พ๏ธ/โ™พ๏ธ or 0/0, you can now apply this rule:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(502).png?alt=media&token=f3804ad3-8d49-4555-a346-84684b58a98b

It is important to note that this is different from quotient rule! It cannot replace quotient rule and cannot be used on problems other than these specific limits. It is called Lโ€™Hopitalโ€™s Rule!ย 

When You Can Use L'Hopitals

When completing a free response question, it is important to show the limits of f(x) and g(x) are separately equal to the needed parameters, as I showed in blue above.ย 

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(503).png?alt=media&token=d7f97f3b-01ae-4f41-854e-a14782fa2126

That is Unit 4! New ways we can apply the derivative rules we know to situations in context. If you see a new situation, donโ€™t panic! Just apply what you know.

continue learning

Slide 1 of 9
Fiveable

Join Our Community

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students!๐ŸŽ‰

Fiveable Logo

2550 north lake drive
suite 2
milwaukee, wi 53211

92% of Fiveable students earned a 3 or higher on their 2020 AP Exams.

*apยฎ and advanced placementยฎ are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

ยฉ fiveable 2020 | all rights reserved.