Calculus - Limit
------------------------------------------------------- Special Case of Limit ---------------------------------------------
 sin 5 x  sin 7 x 
?
x0
6x


1. (91/16 O) lim 
[2]
sin 2 x
?
x
1  cos x
3. (00/16 O) lim
?
x0 2sin 2 x
x sin x
4. (06/2 O) lim 2
?
x0 sin 2 x
sin 7 x  sin 5x
5. (09/12a S) lim
?
x0
6x
2. (95/16 O) lim
[2]
x0
1
]
4
1
[ ]
4
[
[2]
5 x8
 x 1 
6. (14/19 O) lim 

x
 x 
?
[ e5 ]
 3x  1 
 ?
x 3 x  1


x
2
7. (05/9 O) lim 
[ e3 ]
 3  2x 
8. (08/10a S) lim 
 ?
x 5  2 x


x
[ e1 ]
x
2 

9. (15/10a S) lim 1 
 ?
x
 x5
[ e2 ]
------------------------------------------------------- L’ Hôpital’s Rule --------------------------------------------------
tan 1
1. (03/18 O) lim
n
y
n
y
n ?
x4 2
?
x0
sin 5 x
3
2  x   23

?
3. (08/6 O) lim
x 0
2sin x
2x  1
?
4. (12/19 O) lim
x0 sin 2 x
3e4 x  3
?
5. (15/17 O) lim
x0
x
tan
2
ln x 2
?
6. (13/12a S) lim
x1 x  1
2. (07/16 O) lim
[1]
[
1
]
20
[6]
[
ln 2
]
2
[24]
[2]