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
L'Hôpital's Rule
Date________________ Period____
3x
ln ( x + 1)
1) lim
x→1
5 ln x
x−1
2) lim
x→0
f(x)
f(x)
f(x)
10
12
10
10
8
10
8
8
6
8
6
6
4
6
4
4
2
4
2
−2
−8
2
4
6
8
−6
−4
−2
2
4
6
2
8 x
−2
−6
x
−2
−4
−2
−4
−8
2
4
6
8
3) lim+ 5 x 2 ln x
6) lim
x→ ∞
7) lim+ 5 ⋅ (tan x)
sin x
x→0
(
2
2
8) lim+ 3 x
)
x
x→ ∞
π
2
6) lim
0
2
x→ ∞
sin x
x→0
x
9) lim
x→0
e −e
x
−x
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x
10) lim+
x→0
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
sin (2 x)
(
2
x
x
−
x−1
x+1
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.
8 x
0
7) lim+ 5 ⋅ (tan x)
x→0
6
4) lim 4 x ⋅ e − x
5) lim (3sec x − 3tan x)
x→
4
3
x→0
x
x
−
x−1
x+1
2
−4
0
π
2
−2
−2
3) lim+ 5 x 2 ln x
x→ ∞
5) lim (3sec x − 3tan x)
−4
−2
4) lim 4 x ⋅ e − x
x→0
−6
x
5
x→
3x
ln ( x + 1)
12
2
−4
Name___________________________________
Evaluate each limit using L'Hôpital's Rule.
f(x)
−6
Kuta Software - Infinite Calculus
x
9) lim
x→0
e −e
x
−x
x
10) lim+
x→0
−x
e +e
sin (2 x)
∞ *
2
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