Guillaume De l'H

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3.7 Indeterminate forms and LHospitals Rule
Guillaume De l'Hôpital 1661 - 1704
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Indeterminate forms
Consider or
Zero divided by zero can not be evaluated. The
limit may or may not exist, and is called an
indeterminate form.
In the case of the first limit, we can evaluate
it by factoring and canceling
This method does not work in the case of the
second limit.
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LHospitals Rule
Suppose f and g are differentiable and g(x) ? 0
near a (except possible at a). Suppose that
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LHospitals Rule Examples
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Example
If its no longer indeterminate, then STOP
differentiating!
If we try to continue with LHôpitals rule
which is wrong!
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On the other hand, you can apply LHôpitals rule
as many times as necessary as long as the
fraction is still indeterminate
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Indeterminate Products
Rewrite as a ratio!
but if we want to use LHôpitals rule
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Indeterminate Differences
Rewrite as a ratio!
If we find a common denominator and subtract, we
get
Answer
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Indeterminate Powers
Indeterminate Forms
Evaluating these forms requires a mathematical
trick to change the expression into a ratio.
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Indeterminate Forms
Example