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04 - LHopitals Rule

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Kuta Software - Infinite Calculus
Name___________________________________
L'Hôpital's Rule
Date________________ Period____
Evaluate each limit using L'Hôpital's Rule.
1) lim
x→1
5 ln x
x−1
2) lim
x→0
3x
ln ( x + 1)
f(x)
f(x)
12
10
10
8
8
6
6
4
4
2
2
−6
−4
−2
−8
2
4
6
8
−6
−4
−2
2
6
8 x
−2
x
−2
−4
3) lim+ 5 x 2 ln x
4) lim 4 x ⋅ e − x
5) lim (3sec x − 3tan x)
x
x
6) lim
−
x→ ∞ x − 1
x+1
x→0
x→ ∞
π
x→
2
7) lim+ 5 ⋅ (tan x)
4
sin x
x→0
(
2
2
)
8) lim+ 3 x x
x→0
Evaluate each limit. Use L'Hôpital's Rule if it can be applied. If it cannot be applied, evaluate using
another method and write a * next to your answer.
x
e −e
9) lim
x→0
x
−x
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x
−x
e +e
10) lim+
x→0
sin (2 x)
Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
L'Hôpital's Rule
Date________________ Period____
Evaluate each limit using L'Hôpital's Rule.
1) lim
x→1
5 ln x
x−1
2) lim
x→0
3x
ln ( x + 1)
f(x)
f(x)
12
10
10
8
8
6
6
4
4
2
2
−6
−4
−2
−8
2
4
6
8
−6
−4
−2
2
4
6
8 x
−2
x
−2
−4
3
5
3) lim+ 5 x 2 ln x
4) lim 4 x ⋅ e − x
x→0
x→ ∞
0
0
5) lim (3sec x − 3tan x)
π
x→
2
0
(
2
2
x
x
6) lim
−
x→ ∞ x − 1
x+1
)
2
7) lim+ 5 ⋅ (tan x)
sin x
x→0
8) lim+ 3 x x
x→0
3
5
Evaluate each limit. Use L'Hôpital's Rule if it can be applied. If it cannot be applied, evaluate using
another method and write a * next to your answer.
x
e −e
9) lim
x→0
x
−x
x
−x
e +e
10) lim+
x→0
sin (2 x)
∞ *
2
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Worksheet by Kuta Software LLC