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SOAL MATEMATIKA LIMIT FUNGSI TRIGONOMETRI
1.
lim x→
tan5 x 3 x
0
lim
Jawaban :
{
x→
lim tan tan 5 x x → 0
0
(
5 x
.
3 x
)
}{ } 5
.
5 x
tan tan 5 x 5 x
3
5
1.
3
lim tan5 x x → 0
2.
=
3 x
lim ❑ x→
0
tan tan 4
3
x
2 x
lim
Jawaban :
{
5
x→
lim tan tan 4 x x → 0
4
0
(
4 x
4 x .
2 x
)
}{ } 4
.
x
tan tan 4 x
2
4
1.
2
lim tan tan 4 x x → 0
3.
2 x
lim ❑ x→
0
=
2
=2
tan tan 8 x 4 x
Jawaban :
{
4
lim x→
lim tan tan 8 x x → 0
8 x
0
(
tan tan 8 x 8 x 8 x
}{ } 8
.
4
.
2 x
)
8
1.
4
lim tan8 x
8
x → 0
4
=
x
4
=2
lim 3 x x → 0
4.
sin 4 x
(
lim
Jawaban :
0
x→
4
3 x
x
sin 4 x
.
4 x
)
{ }{ } lim 4 x
3
x → 0
.
sin 4 x
4
3
1.
4
lim 3 x
x → 0
sin 4 x
3
=
4
lim 16 x x → 0
5.
sin8 x
lim
Jawaban :
x→
0
(
8 x sin 8 x
8 x
{ }{ } lim 8 x x → 0
sin 8 x
16
.
8
16
1.
8
lim 16 x
x → 0
sin 8 x
16
=
8
= 2
lim sin4 x + tan 3 x − sin5 x
6.
x → 0
2 x
)
16 x .
lim sin4 x + tan 3 x − sin5 x x → 0
Jawaban :
lim x→
0
(
2 x
sin 4 x 2 x
) +
(
2.
(
lim x→
0
tan 3 x 2 x
)
lim sin 4 x x → 0
4 x
+
2
2
0
x→
(
3
3
2.1+
) -
lim
.
(
sin5 x 2 x
)
lim tan3 x x →
0
3 x
)
-
5 2
(
lim sin5 x x → 0
5 x
5 .
1-
2
. 1 = 1
lim sin 8 x + tan 4 x − sin2 x
7.
x →0
2 x
lim sin 8 x + tan 4 x −sin 2 x x → 0
Jawaban :
lim x→
0
(
2 x
sin 8 x 2 x
) +
(
2.
lim x→
0
lim sin 8 x x → 0
8 x
(
)
tan 4 x 2 x
) -
+ 2 .
lim x→
(
0
(
sin 2 x 2 x
lim tan 4 x x →
0
4 x
)
) - 1
2.1+2.1–1.1=5 lim sin 9 x + tan 3 x− sin 3 x
8.
x →0
3 x
lim sin9 x + tan 3 x −sin 3 x
Jawaban :
lim x→
0
(
x → 0
sin 9 x 3 x
3 x
) +
lim x→
0
(
tan 3 x 3 x
) -
lim x→
0
(
sin3 x 3 x
)
(
lim sin 2 x x →
0
2 x
)
)
(
3.
lim sin 9 x x → 0
9 x
)
(
+ 1 .
lim tan3 x x →
0
3 x
)
- 1
(
lim sin 3 x x →
0
3 x
)
3.1+1.1–1.1=3 lim sin 14 x + tan7 x −sin 7 x
9.
x →0
7 x
lim sin 14 x + tan 7 x −sin7 x x → 0
Jawaban :
lim x→
0
(
7 x
sin14
x
7 x
) +
(
2.
(
lim x→
0
tan 7 x 7 x
)
lim sin 14 x x → 0
14 x
) -
lim 0
x→
(
+ 1 .
(
sin7 x 7 x
lim tan7 x x → 0
7 x
)
)
- 1
(
lim sin7 x x →
0
7 x
)
2.1+1.1–1.1=3 lim sin 24 x + tan 12 x + sin6 x
10.
x → 0
6 x
lim sin 24 x + tan 12 x + sin 6 x x → 0
Jawaban :
lim x→
0
(
6 x
sin24 x 6 x
4.
(
) +
lim x→
0
lim sin 24 x x → 0
24 x
(
)
tan 12 x 6 x
) +
+ 2 .
(
lim sin 4 x + tan 3 x
11.
x
x→
0
(
sin 6 x 6 x
lim tan12 x x →
4.1+2.1+1.1=7 x → 0
lim
0
12 x
)
)
+ 1
(
lim sin 6 x x →
0
6 x
)
lim sin 4 x + tan 3 x
Jawaban :
x → 0
lim sin 6 x + tan 4
12.
=
x
lim x→
0
(
4 x + 3 x
(
6 x + 4 x
(
9 x + 3 x
(
8 x + 4 x
(
9 x + 3 x
(
6 x + 6 x
x
) =
7 x
) =
10 x
) =
12 x
) =
12 x
) =
12 x
) =
12 x
x
= 7
x
x → 0
x
lim sin 6 x + tan 4
Jawaban :
x
x → 0
x
=
lim x→
0
x
x
= 10
lim sin 9 x + tan 3 x
13.
x → 0
x
lim sin 9 x + tan 3 x
Jawaban :
x → 0
x
=
lim
=
lim
=
lim
x→
0
x
x
= 12
lim sin 8 x + tan 4 x
14.
x → 0
6 x
lim sin 8 x + tan 4 x
Jawaban :
x → 0
6 x
x→
0
6 x
6 x
= 2
lim sin 9 x + tan 3 x
15.
x → 0
3 x
lim sin 9 x + tan 3 x
Jawaban :
x → 0
3 x
x→
0
3 x
3 x
= 4
lim sin 6 x + tan 6 x
16.
x → 0
12 x
lim sin 6 x + tan 6 x
Jawaban :
x → 0
lim sin 5 x + tan 6 x
17.
x → 0
x
6 x
=
lim x→
0
12 x
12 x
= 1
lim sin 5 x + tan 6 x
Jawaban :
x → 0
=
x
lim x→
0
(
5 x + 6 x
(
3 x + 6 x
(
7 x + 4 x
x
) =
11 x
) =
9 x
) =
11 x
= 11
x
lim sin 3 x + tan 6 x
18.
x → 0
2 x
lim sin 3 x + tan 6 x
Jawaban :
x → 0
=
2 x
lim x→
0
2 x
9
=
2 x
2
lim sin 7 x + tan 4 x
19.
x → 0
3 x
lim sin 7 x + tan 4 x
Jawaban :
x → 0
=
3 x
lim x→
0
3 x
11
=
3 x
2
lim sin 15 x + tan 5 x
20.
x → 0
4 x
lim sin 15 x + tan 5 x
Jawaban :
x → 0
lim
=
4 x
x→
0
(
15 x + 5 x 4 x
) =
lim cot 5 x
21.
x → 0
cot 10 x
lim cot 5 x
Jawaban :
x → 0
cot 10 x
lim x→
0
[
5 x tan5 x
=
lim x→
0
tan 10 x 10 .
10
.
5
[
1 tan5 x
[ ] [ x→
1
]
]
lim 5 x
2.
tan 10 x .
0
tan 5 x
2.1.1 = 2
.
lim tan 10 x x → 0
10
]
20 x 4
x
= 5
lim cot 3 x
22.
x → 0
cot 9 x
[
lim cot5 x
Jawaban :
x → 0
x→
=
cot 10 x
lim 0
[
3 x tan3 x
lim x→
tan 9 x 9 .
.
9
3
0
1 tan3 x
tan 9 x .
1
]
[ ] [ lim 3 x
2.
]
x → 0
.
tan 3 x
lim tan 9 x x → 0
9
]
3.1.1 = 3 lim cot 6 x
23.
x → 0
cot 36 x
[
lim cot 5 x
Jawaban :
x → 0
x→
=
cot 10 x
lim 0
[
6 x tan 6 x
lim x→
0
.
36
tan 6 x
6
[ ] [ lim 6 x
6.
tan 36 x .
x→
1
]
]
tan 36 x 36 .
1
0
.
tan 6 x
lim tan 36 x x → 0
36
6.1.1 = 6 lim cot 16 x
24.
x → 0
cot 8 x
lim cot 16 x
Jawaban :
x → 0
x→
=
cot 8 x
lim 0
[
16 x tan16 x
lim x→
tan 8 x .
8
0
8 .
16
[
]
1 tan16 x
tan 8 x .
1
]
]
1
.
2
[
lim 16 x x → 0
.
tan 16 x
1
] [
lim tan 8 x x → 0
8
]
1
.1.1 =
2
2
lim cot 7 x
25.
x → 0
cot 49 x
[
lim cot 7 x x → 0
Jawaban :
x→
=
cot 49 x
lim 0
[
7 x tan7 x
lim
tan 49 x .
49
0
x→
1
tan 49 x
tan7 x
.
1
]
49 .
7
[ ] [ lim 7 x
7
7
.
]
x→
0
.
tan 7 x
.1.1 =
lim tan 49 x x → 0
49
]
7
lim cot 9 x
26. .
x →0
cot72 x
[
lim cot 9 x
Jawaban :
x → 0
lim x→
=
cot72 x
0
[
9 x tan 9 x
lim x→
0
tan 72 x 72 .
72
.
9
1
tan 72 x
tan 9 x
8
lim cot 6 x
27.
x → 0
cot 30 x
.
[ ] [ x→
1
]
]
lim 9 x
8
.
0
tan 9 x
.1.1 =8
.
lim tan 72 x x → 0
72
]
[
lim cot 6 x
Jawaban :
x → 0
lim x→
=
cot 30 x
0
[
6 x tan 6 x
lim x→
0
tan 30 x 30 .
30
.
6
1
tan 30 x
tan 6 x
.
1
]
[ ] [ lim 6 x
5
.
x→
]
0
.
tan 6 x
lim tan 30 x x → 0
30
]
5.1.1 =5 lim cot 6 x
28.
x → 0
cot 18 x
[
lim cot 6 x
Jawaban :
x → 0
lim x→
=
cot 18 x
0
[
6 x tan 6 x
lim x→
0
tan 18 x 18 .
18
.
6
1
tan 18 x
tan 6 x
.
1
]
[ ] [ lim 6 x
3
.
x→
]
0
.
tan 6 x
lim tan 18 x x → 0
18
]
3.1.1 =3 lim cot 6 x
29.
x → 0
cot 56 x
[
lim cot 6 x
Jawaban :
x → 0
lim x→
=
cot 56 x
0
[
6 x tan 6 x
lim x→
0
tan 56 x 56 .
56
.
6
1
tan 56 x
tan 6 x
.
[ ] [ x→
1
]
]
lim 6 x
9
.
0
tan 6 x
.
lim tan 56 x x → 0
56
]
9.1.1 =9 lim cot 11 x
30.
x → 0
cot 121 x
lim cot 6 x
Jawaban :
x → 0
x→
=
cot 56 x
lim 0
[
11 x tan11 x
lim x→
tan 121 x .
121
11
.
[
0
[
1 tan11 x
121 .
11
Jawaban :
32.
1
]
]
lim 11 x x → 0
tan 11 x
11.1.1 =11 31. Hitunglah,
tan 121 x .
] [ .
lim tan 121 x x →0
121
]
Jawaban :
33.
SOAL LIMIT FU!SI T"I!OOM#T"I SO$A" JOSUA F#LI% SIMAJUTA&
%I MI$A 1
ULA!A 'A"IA 1 : 50 ULA!A 'A"IA 2 : 31
TT(
)..........................* ).......................*
TT(
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