1
King Abdul Aziz University Faculty of Sciences Mathematics Department Math 110 Workshop 8 Section 2.3
Professor Hamza Ali Abujabal [email protected]
1) 3
lim ( 2 2 1)
x x x
A 3
B 3
C 11
D 13
2) 2
lim(32 4)
x x x
A 10
B 2
C 4
D 10
3) 2 3
lim(1 3 5)
x x x
A 1
B 1
C 3
D 13
4) 3 2
lim (22 3 5)
x x x
A 11
B 5
C 1
D 1 5)
2 2
lim 2
2
x
x
x
A 0
B 1
2
C 2
D 1 2 6)
3 2 2
lim 5
1
x
x
x
A does not exist
B 9
5
C 11
5 D 13
5 7)
2 0 2
3 5
limx 3
x x
x
A does not exist
B 5
3
C 5
3 D 5
8) 2
1
lim 1
5
x
x
x x
A does not exist
B 2
3
C 0
D 1
9) 3
lim1 10 7
x x x
A does not exist
B 3
C 4
D 5 10)
2 1
1 ( 4)
lim 2
x
x x
A does not exist
B 8
27
C 8
3
D 8 27
2
11)
1
lim 8 2
x x
A does not exist
B 3
10
C 3
4
D 3
10 12)
2 4
lim 3 5
x
x x
x
A does not exist
B 4
9
C 4
9 D 8
9 13)
2 4
lim 4 5
x
x x
x
A does not exist
B 0
C 4
3 D 8
9 14)
1 1
4
3 (2 5)
lim 4
x
x x
A does not exist
B 0
C 2
9 D 2
9 15)
3 2
0 2
lim 5
x
x x
x
a 5
b 5
c
10
d 0
16) 6 2
lim 6
36
x
x
x
a 12
b 1
12 c 1
8 d 0 17)
2 6
lim 36
6
x
x
x
a 12
b 1
12 c 8
d 0
18) 6 2
lim 6
36
x
x
x
a 12
b 1
8
c 1
12
d 0 19)
3 3
lim 27
3
x
x
x
a 27
b 1
27 c 18
d does not exist
20) 3 3
lim 3
27
x
x
x
a 27
b 1
27 c 1
18 d does not exist
3
21) 2 3
lim 2
8
x
x
x
a 12
b 1
12 c 1
8 d does not exist 22)
3 2
lim 8
2
x
x
x
a 12
b 1
12 c 8
d does not exist 23)
2 4
3 4
limx 4
x x
x
a 5
b 8
c 5
d does not exist 24)
2 3 2
4 21
limx 8 15
x x
x x
a 5
b 1
5
c 5
d does not exist
25) lim0 2
1 (1 )
x
x
x
a 1
2
b 1
2 c 0
d does not exist 26)
3 2
6 2
limx 2
x
x
a 1
12
b 12
c 0
d does not exist 27)
0
25 5
xlim x
x
a 10
b 1
10
c 10
d 1 10 28)
lim 0
25 5
x
x
x
a 10
b 1
10
c 10
d 1 10 29)
2
lim 2
2 6
x
x
x
a does not exist
b 0
c 1
4 d 4 30) 2
2 6
lim 2
x
x
x
a does not exist
b 0
c 1
4 d 4
4
31) lim 3
2 1
x x
a does not exist
b 0
c 1
2 d 2 32) If 2x f x( )3x28, then
2
lim ( )
x f x
a does not exist
b 4
c 0
d 4 33)
0
lim cos( 1)
x x x
x
a does not exist
b 0
c
d 1 34)
0
lim sin( )1
x x
x
a does not exist
b
c 0
d 1 35) If
2 1
( ) 1
1
x f x x
x
, then
lim ( )0
x f x
a does not exist
b 1
c 0
d 1 36) If 4(x 1) f x( )x3 x 2, then
lim ( )1
x f x
a does not exist
b 1
c 0
d 4 37) If
3
( ) 4
lim 3
1
x
f x
x
, then
3
lim ( )
x f x
a 0
b 10
c 2 d 3 38)
1 1
2
2 (3 4)
lim 2
x
x x
A does not exist
B 3
C 3
4 D 3
4 39)
3 0
( 1) 1 limx
x
x
A does not exist
B 3
C 3
D 0
40) If 2
1
( ) 3
lim 1
5 ( )
x
f x x
x f x
, then
1
lim ( )
x f x
a 1
b 1
3
c 2
3
d 3 41)
2 4 2
6 8
lim 20
x
x x
x x
a does not exist
b 0
c 2
9 d 1
5
42)
3 2 2
lim 8
6
x
x
x x
a does not exist
b 12
5
c 8
5
d 12 43)
2
2 1
lim 2 2
4
x
x x x
x
a does not exist
b 6
5 c 1
d 6
5 44)
2 2 2
4 6 4
lim 2 8
x
x x
x
a does not exist
b 5
c 5
4 d 5
4 45)
2
5 3
1
2 3
xlim
x x
x x
a does not exist
b 2
c 2
d 4 46)
2
3
2 1( 9)
limx (2 3)( 3)
x x
x x
a 7
9
b 2
3 c 7
3 d
2 7 3 47)
1
3 2 1
limx 1
x
x
a 1
b 1
c 2
2 d 2 48)
2 0
( 1) 1 limx
x
x
a 0
b 2
c 1
2 d 2 49)
1
2 2 2
limx 3 2 1 x
x
a 3
2
b 2
3 c 1
3 d 1
3 50)
2
3 2 5
limx 2
x
x
a 1
6
b 3
c 1
3 d 1
3 51)
2 1 2
3 2
lim 1
x
x x
x
a 0
b
c does not exist
d 1
6
52) If lim ( ) 2
x kf x
and lim ( )
3
x k g x
, then lim
( )
xk g x
a 1 3
b 1
3
c 3
d 3
4 53)
0
4 2
limx
x
x
a 0
b 1
c 1
4 d 4 54)
2 1
5 6
lim 1
x
x x
x
a 0
b 1
c does not exist
d 7 55)
1 1
0
( 3) 3
limx
x x
A 1
9 B 0
C 1
3
D 1 9 56) If
1
lim ( ) 3
x f x
,
1
lim ( ) 4
x g x
,
1
lim ( ) 1
x h x
, then
1
5 ( )
lim ( )
2 ( )
x
f x h x
g x
a 23 8
b 7
8 c 3
d 23
8 57) If
1
lim ( ) 4
x g x
and
1
lim ( ) 1
x h x
, then
1
lim ( ) ( )
x g x h x
a 2
b 2
c 2
d 3 58) If
1
lim ( ) 3
x f x
,
1
lim ( ) 4
x g x
,
1
lim ( ) 1
x h x
, then
lim 2 ( ) ( ) ( )1 x f x g x h x
a 24
b 48
c 12
d 24
