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Section 4.5 – Indeterminate Forms and L’Hospital’s Rule
1.
L’Hospital’s Rule 
Suppose f and g are differentiable and
0
)
(
≠
′
x
g
Suppose that
0
)
(
lim
=
→
x
f
a
x
and
0
)
(
lim
=
→
x
g
a
x
∞
=
→
)
(
lim
x
f
a
x
and
∞
=
→
)
(
lim
x
g
a
x
Then
)
(
)
(
lim
)
(
)
(
lim
x
g
x
f
x
g
x
f
a
x
z
x
′
′
=
→
→
Examples a)
x
z
x
e
x
3
lim
→
b)
2
ln
lim
x
x
x
∞
→
c) #16
x
x
x
π
sin
ln
lim
1
→
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View Full Document d) #32
)
cot
(csc
lim
0
x
x
x

→
Note: This is not in the form for L’Hospital’s rule; algebraically
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This note was uploaded on 03/20/2008 for the course MA 141 and 24 taught by Professor Dempster/mccolum during the Spring '08 term at N.C. State.
 Spring '08
 dempster/mccolum
 Math

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