x - Kuta Software

©t t2r091r3e mKuuotNaQ jSYoRfHt1weaArve0 uL3LfCq.7 e WAhlclN 7r9iugrhUt0sW WrGe6s7eMrvvyeadg.J i nMla1diei pwOibtPho bIXnSf8iZn5iItAe1 iCVaglnctuxlnujsm.S Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
L'Hôpital's Rule
Evaluate each limit using L'Hôpital's Rule.
Date________________ Period____
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 2 4 6 8
−2
x
−8 −6 −4 −2 2 4 6 8
−2
−4
x
3) lim 5x 2 ln x 4) lim 4x ⋅ e −x
x →0 + x → ∞
5) lim
x → π 2
(3sec x − 3tan x)
( 6) lim
x2
x → ∞ x − 1 − x 2
) x + 1
7) lim 5 ⋅ (tan x) sin x 8) lim
x →0 + x →0 +
3x x
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.
9) lim
x →0
e x − e −x
x
10) lim
x →0 +
e x + e −x
sin (2x)

©C o2E0O1Q37 BKsuEt2az cSBoefAtawmaKrcel pLqLHCt.9 F XAdlwl4 5rkiUgVhAt4sB jrWessmedrVvje9d0.1 1 nMjajdIeX zw7iwtUho lIPngfLienDiqtweB NCeanlzcHu0lCuwsY.k Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
L'Hôpital's Rule
Evaluate each limit using L'Hôpital's Rule.
Date________________ Period____
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 2 4 6 8
−2
x
−8 −6 −4 −2 2 4 6 8
−2
−4
x
5
3
3) lim
x →0 +
0
5x 2 ln x
4) lim 4x ⋅ e −x
x → ∞
0
5) lim
x → π 2
0
(3sec x − 3tan x)
( 6) lim
x2
x → ∞ x − 1 − x 2
) x + 1
2
7) lim
x →0 +
5 ⋅ (tan x) sin x
8) lim
x →0 +
3x x
5
3
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.
9) lim
x →0
2
e x − e −x
x
10) lim
x →0 +
∞ *
e x + e −x
sin (2x)
Create your own worksheets like this one with Infinite Calculus. Free trial available at KutaSoftware.com