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

1 min readβ€’june 22, 2020

Meghan Dwyer

Meghan Dwyer


AP Calculus AB/BC ♾️

279Β resources
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Indeterminate Forms

Remember those times when you were solving limits at infinity, and you would come out with an answer that looked like ♾️/♾️ 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 ♾️/♾️ 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 L’Hopital’s Rule!Β 

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.Β 
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, don’t panic! Just apply what you know.
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