Indeterminate Forms and L’Hopital’s Rule

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Presentation transcript:

Indeterminate Forms and L’Hopital’s Rule

In evaluating functions often you need to know how a function behaves near a number is undefined at x = 1 Need to know how it behaves near 1 Called an Indeterminate for of type 0/0

Indeterminate form of type ∞/∞

L’Hopital’s Rule If f and g are differentiable and g’(x)≠0 near a, then May use more than once if necessary

DO NOT APPLY L’Hopital’s Rule unless an Indeterminate form is produced For instance, the following application of L’Hôpital’s Rule is incorrect. The reason this application is incorrect is that, even though the limit of the denominator is 0, the limit of the numerator is 1, which means that the hypotheses of L’Hôpital’s Rule have not been satisfied.

Practice Find the following limits 1) 2)

3) 4) 5)