L hopitals rule

1. AP Calculus BC L’Hopital’s Rule

2. L’Hopital’s Rule FDWK 8.2, Larson 7.7 Basic formula: Used to evaluate limits of indeterminate forms . It can also be used with the forms . It can be used repeatedly, but only when the new form is also indeterminate. Note that it is different than the quotient rule.  

3. Examples Indeterminate Form 0/0 Indeterminate Form ∞/∞ Applying L’Hopital’s Rule more than once Indeterminate Form 0•∞ convert to 0/0 or ∞/ ∞ Indeterminate Form 1 ∞ use logarithmic differentiation Indeterminate Form 0 use logarithmic differentiation Indeterminate Form ∞-∞ find a common denominator

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9. Wrapping It Up You can only use L’Hopital’s Rule when the basic criteria are met Even though there are many indeterminate forms, we only apply L’Hopital’s Rule to the basic cases of 0/0 or ∞/ ∞ The other types of indeterminate forms must first be converted into 0/0 or ∞/ ∞, before L’Hopital’s Rule can be applied