Gioi han cua ham so

Giíi h¹n_Qu¸ch Duy TuÊn
1)
1
352
lim
23
23
1
−+−
+−
→
xxx
xx
x
→ -2
2)
32
38
lim
2
1
−+
−+
→
xx
x
x
→1/24
3)
2
24

lim
3
2
−
−
→
x
x
x
→ 1/3
4)
1
75
lim
2
3
23
1
−
+−−
→
x
xx
x
→ -11/24
5)[§HQG_A97]
x
xx
x
3

0
812
lim
−−+
→
→ 13/12
6)[§HSPHN_B00]
1
57
lim
2
3
1
−
−−+
→
x
xx
x
→ 7/12
7*)[§HTL_01]
2
3
0
3121
lim
x
xx
x
+−+

→
→ 1/2
(Thªm bít 1 + x)
8)
x
ax
n
x
11
lim
0
−+
→
(a ≠ 0) → a/n
(§Æt t =
n
ax
+
1
)
9)
x
xx
x
5
1312
lim
53
0
+−+

→
→ 1/75
10)[§HSPHNII_A99]
1
212
lim
5
4
1
−
−+−
→
x
xx
x
→7/10
11)[§HQG_A98]
1
23
lim
3
1
−
−−
→
x
xx
x
→ 3/2
12)

x
x
x
2
3sin
lim
0
→
→ 3/2
13)
xtg
x
x
4
3sin
lim
0
→
→ 1/2
14)
x
xtgx
x
5
23sin
lim
0
+
→
→ 1

15)
2
0
2coscos1
lim
x
xx
x
−
→
→ 5/2
16)
2
0
2coscos4cos
lim
x
xxx
x
−
→
→ -11/2
17)
x
ee
bxax
x
−
→
0

lim
→ a – b
18) [HVKTQS_97]
2
0
sin
lim
x
xtgx
x
−
→
→ 1/2
19*)[§H TN_A97]
2
sin
cos
2
cos
lim
2
0
x
x
x







→
π
→ π
20)[§HSP Vinh_B99]
xx
xx
x
2cos2sin1
2cos2sin1
lim
0
−+
−−
→
→ -1
21)
x
xx
x
sin
243
lim
0
−−+
→
→ -1/4
22*)[§HAN_00]
x
xxx

x
7sin
7cos5cos3cos1
lim
2
0
−
→
→ 1
23)
3
23
2
12
1
lim
+++
++
−∞→
xxx
xx
x
→ -1/
3
2

24)
)1(lim
2
xxx

x
+++
−∞→
→ -1/2
25)[§HGT_95]
1
21
lim
3
1
−
−+
→
x
x
x
→3/2
2
,
3
x
=t
26)[HVNH_98]
1
12
lim
1
−
−−
→

x
xx
x
→ 1/2
27)[§H§N_AB99]
1
132
lim
2
1
−
+−
→
x
xx
x
→ 5/8
28)[§HH§_D01]
1
533
lim
3
2
1
−
+−+
→
x
xx
x

→ -1/4
29)[§HSPV_01]
x
xxx
x
3
3
3
2
0
11
lim
+−++
→
→ 1/3
30)[§HHH_98]
xx
x
xtg
sin
1
2
0
)1(lim
+
→
→ e
31)[§HHH_99]
x
ee

xx
x
sin
lim
sin2sin
0
−
→
→ 1
32)[§HTM_99]
2
2
0
cos1
lim
x
xx
x
−+
→
→ 1
33)[§HQGHN_D00]
x
xx
x
sin
112
lim
3
2

0
+−+
→
→ 1
34)[§HSPHN_D00]
)1sin(
2
lim
3
1
+
++
−→
x
xx
x
→ 4
35)[§H§§_AV00]
xx
xx
x
+−−
+−−
→
11
11
lim
2
0
→ 1/2

36)[C§SPMGTW1_01]
nx
xtg
nx
+
−→
π
lim
→ π, x+n=t
37)[§H§§_BD00]
x
x
x
11sin
7cos1
lim
2
0
−
→
→ 49/242
38)[§H§§_A00]
x
xx
x
11sin
7cos5cos1
lim
2
0

−
→
→ 37/121
39)[§HSP2_A00]
a)
)
4
(.2lim
4
xtgxtg
x
−
→
π
π
→ 1/2
b)
2
0
cos3
lim
2
x
x
x
x
−
→
→ 1/2+ln3
( Thªm h»ng sè 1, sau ®ã ®Æt

t
x
=−
13
2
)
40)[§HHH_01]
11
1sincos
lim
2
44
0
−+
−−
→
x
xx
x
→ - 4
41)[C§SPHN_D00]
x
xx
x
2
3
0
sin
coscos
lim

−
→
Giíi h¹n_Qu¸ch Duy TuÊn
→ -1/12
42)[§HQGHN_A95]
2
2
0
4sinsin2sin
lim
x
xxx
x
−
→
→ 0
43)[§HGT_97]
x
x
x
1
coslim
0
→
→ 0
( Sö dông giíi h¹n kÑp -
x
x
xx
≤≤

1
cos
)
44)[BCVT_99]
xx
xx
x
sin
sin
lim
+
−
∞→
→ 1
( Chia c¶ tö vµ mÉu cho x,
0
sin
lim
=
∞→
x
x
x
)