4'4 Indeterminate Forms and LHospitals Rule

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4.4 - Indeterminate Forms and LHospitals Rule
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LHospitals Rule
Suppose f and g are differentiable functions and
g'(x) ? 0 near a (except possibly at a). Suppose
that or that Then if the limit on the
right side exists (or is 8).
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LHospitals Rule
In simpler terms, if after substituting in a,
Then if the limit on the right side exists
(or is 8).
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LHospitals Rule if f(a) f(b) 0
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Indeterminate Forms
1. 0 / 0 or 8 / 8 Strategy Apply
LHospitals Rule Directly 2. 0
8 Strategy Apply LHospitals Rule to
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Indeterminate Forms
3. 8 - 8 Strategy Try factoring,
rationalizing, finding common denominator, etc.
to get into form 1 above. 4. 00 or 80 or
18 Strategy Use f (x)g(x) eg(x) ln f (x)
or ln y ln f(x)g(x). Then,