L’Hopital’s rule A new way to take limits. If f and g are continuous at a but then the limit will be the indeterminant form. L’Hopital’s rule says that.

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Presentation transcript:

L’Hopital’s rule A new way to take limits

If f and g are continuous at a but then the limit will be the indeterminant form. L’Hopital’s rule says that if you get indeterminant form, you can take the derivative of the top and bottom (NOT a quotient rule) and then reevaluate the limit. That is,

L’Hopital’s Rule If and f’(a) and g’(a) exist (with g’(a)≠0) then (stronger form says if you get indeterminant form again, go ahead and take a derivative again)

Proof: Start at the end Remember:

This makes limits very easy! Find the following