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L’Hosptital’s Rule

# L’Hosptital’s Rule - LHospitals Rule Look at these...

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L’Hospital’s Rule

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Look at these examples After subbing in we get either , And neither of these makes any sense These are special cases We use a new rule L’Hospital’s Rule
L’Hospital’s Rule Only works when and and count too because

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L’Hospital’s Rule If or then We differentiate the function in the numerator and the function in the denominator separately!! WE DON’T USE THE QUOTIENT RULE!
e.g.1 compute the limit Solution This gives , so L’Hospital’s Rule applies 2 lim 1 x x x  2 1 lim lim 0 2 1 1 x x x x x  

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Examples 1. Which gives so apply the rule Remember that this is NOT true if we had 2. which is of the form 3.
4. compute the limit This is a indeterminate form, so L’Hôpital’s Rule applies 5 4 5 3 2 1 3 5 3 lim 4 2 5 1 x x x x x x x 0 0 5 4 4 3 5 3 2 4 2 1 1 3 5 3 5 12 5 1 lim lim 8 4 2 5 1 20 6 10 x x x x x x x x x x x x x

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6.
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• Spring '14
• Limits, lim, Limit of a function, Indeterminate form, 10 0 L

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