L’Hopital (Lo-pee-tal) was a French mathematician who wrote the first calculus textbook Remember back in the limits unit when we evaluated a limit and.

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Presentation transcript:

L’Hopital (Lo-pee-tal) was a French mathematician who wrote the first calculus textbook Remember back in the limits unit when we evaluated a limit and got an indeterminate form, we had to use algebra to rewrite the equation, then use substitution again. L’Hopital’s rule (which was actually discovered by Bernoulli) gives us another (and better) way to find the limit

L’Hopital’s rule is used to evaluate limits of certain types of quotients of two functions If the quotient has an indeterminate form, you can replace with

You need to be careful to take derivatives of numerator and denominator separately! Do not use the quotient rule!!

You can only use L’Hopital’s rule if you have the indeterminate form 0/0 or ∞/∞!!! No other time!

Evaluate the following

Sometimes we may need to repeat ourselves. Sometimes we may need to repeat ourselves.

If you get some other indeterminate form, you can still use L’Hopital if you first rewrite it so it comes out 0/0 or ∞/∞

Use L’Hopital’s rule to evaluate

If you get 0 0, then take ln Now exponentiate (undo the ln)