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March 18, 2016 Editor Hendry. P 1
1
PENDAHULUAN
2
PEMBAHASAN
3
PENUUP
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LOGO
March 18, 2016 Editor Hendry. P 2
STANDAR KOMPETENSI
MEN!!UNA"AN "#NSEP L$M$
%UN!S$ DAN U&UNAN %UN!S$
DALAM PEME'AHAN MASALAH
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March 18, 2016 Editor Hendry. P 3
"#MPEENS$ DASA&
1.MEN(ELAS"AN SE'A&A $NU$$%
A&$ L$M$ %UN!S$ D$SUAU $$"DAN D$ A" H$N!!A
2.MEN!!UNA"AN S$%A L$M$ %UN!S$
UNU" MEN!H$UN! BENU" A"ENU %UN!S$ AL(ABA& DAN
&$!#N#ME&$
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March 18, 2016 Editor Hendry. P )
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March 18, 2016 Editor Hendry. P *
SEELAH MEMPELA(A&$ BAB $N$,PESE&A D$D$" D$HA&AP"AN
MAMPU MEN(ELAS"AN SE'A&A
$NU$$% A&$ L$M$ %UN!S$
D$SUAU $$" DAN D$ A"
H$N!!A ,MEN!!UNA"AN S$%A
L$M$ %UN!S$ UNU"
MEN!H$UN! BENU" A" ENU%UN!S$ AL(ABA& DAN
&$!#N#ME&$
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LOGO
March 18, 2016 Editor Hendry. P 6Materi Kelas XI Semester 4
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L$M$ %UN!S$ AL(ABA&1
E#&EMA L$M$2
L$M$ %UN!S$ &$!#N#ME&$3
DAL$L LH#SP$AL4
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March 18, 2016 Editor Hendry. P 8
Limit = Pendekatan
Berarti Limit Fungsi = Pendekatan Nilai Fungsi
Manfaatnya :
Untuk mentukan nilai fungsi yang memiliki nilai tak
Tentu seperti :
[ ] [ ]∞∞∞
∞∞
x0,-,,0
0
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March 18, 2016 Editor Hendry. P -
Daat di/ee/aian denan f(x)Limitax→
)(Limitx
x f ∞→
A. Bent4
1. S45/tit4/i
2. Pe7atoran
3. Peraian /eaan
B. Bent4 Daat di/ee/aian denan
1. Pe5aian anat tertini enye54t2. Peraian /eaan
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March 18, 2016 Editor Hendry. P 10
)(Limitax
x f →
25 E.
24 D.
23 C.
22 B.
21 A.
...)]13)(1[(LimitHitungla 22x
=−+→
x x
BENU"
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March 18, 2016 Editor Hendry. P 11
25
5x5
1)-2.3)(1(2)]13)(1[(xLimit
)]13)(1[(LimitHitungla
22
2x
2
2x
=
=
=+=−+
=−+
→
→
x
x x
#P$#N
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March 18, 2016 Editor Hendry. P 12
∞
=
+
−
→
E.
2 D.
1 C.
2
1 B.
0 A.
...Limit0x
x x
x x
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March 18, 2016 Editor Hendry. P 13
101
01
1
1
Limit
)1(
)1(LimitLimit
0x
0x0x
=+
−
=+
−
=
+
−=
+
−
→
→→
x
x
x x
x x
x x
x x
#P$#N
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March 18, 2016 Editor Hendry. P 1)
22 E.
2 D.
22
1
C.
2
1 B.
2
4
1 A.
.....22
Limit0x
=−−+
→ x
x x
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March 18, 2016 Editor Hendry. P 1*
2
2
1
2
1
22
2
0202
2
22
2
Limit
)22(
2
)22(
)2()2(Limit
22
2x2 x
22Limit
0x
0
0x
==
=−++=−++
=−++
=−++
−−+
−++
−++−−+
→
→
→
x x
x x x
x
x x x
x x
x x
x
x
x x
x
#P$#N
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March 18, 2016 Editor Hendry. P 16
)(LimitBE!"#$x
x f ∞→
0g(x)
f(x)Limit
ma%ag(x)&'aatf(x)&'aat*i%a 3.
-g(x)
f(x)Limit
ma%an'gatif, +'nilaif(x)inggi t't
ang%at%'fii'n i%a'+ali%n/ag(x)
f(x) Limit
ma%a itif, +'nilaif(x)inggi t't
ang%at%'fii'n&ang(x)&'aatf(x)&'aat*i%a .2
g(x)&aitinggi ang%at t'%'fii'n
f(x)&aitinggi ang%at t'%'fii'n
g(x)
f(x) Limit
ma%ag(x)&'aatf(x)&'aat*i%a 1.
/aituaa3&'nganan&i'l'ai% &aat)(
)(Limit
x
x
x
x
x
=
<
∞=
∞=
>
=
=
∞→
∞→
∞→
∞→
∞→ x g
x f
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March 18, 2016 Editor Hendry. P 1+
3 E.
2 D.
1- C.
2- B.
3- A.
...432
34LimitHitungla
23
23
x=
+++−
++−
∞→ x x x
x x x
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March 18, 2016 Editor Hendry. P 1-
1 E.
2
1 D.
0 C.
B. - A.
...2
132Limit
2
x
∞∞
=+
−+∞→ x
x x
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March 18, 2016 Editor Hendry. P 20
"arena Dera9at %:;< = dera9at !:;< dan "oe7i/ien anat tertini %:;<
5erniai Po/iti7, aa
∞=
+
−+
∞→
2
132Limit
2
x x
x x
#P$#N
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March 18, 2016 Editor Hendry. P 21
1 E. D.
0 C.
1- B.
- A.
...24
4234Limit
2
32
x
∞
∞
=
−+
−+−
∞→ x x
x x x
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March 18, 2016 Editor Hendry. P 22
∞=
−+
−+−
∞→
-244234Limit
2
32
x x x x x x
#P$#N
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March 18, 2016 Editor Hendry. P 23
1 E.
0 D.
C.
1- B. - A.
...53
143Limit
24
23
x
∞
∞
=++−
++−∞→ x x x
x x x
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March 18, 2016 Editor Hendry. P 2)
"arena dera9at 7:;< > dera9at :;< aa
053
143Limit
24
23
x=
++−
++−
∞→ x x x
x x x
#P$#N
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March 18, 2016 Editor Hendry. P 2*
5312Limit 1.
ini +'i%utfungiLimitHitungla
x+−−
∞→ x x
Lihat Haaan 5eri4t
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March 18, 2016 Editor Hendry. P 26
6 x
6 x
+ax
+ax x6 x +axLimit i%a*a&i
'%a7an '%alian&'ngan&i%ali%anauitu8al
9x +
+−
+
++++
→
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March 18, 2016 Editor Hendry. P 2+
1 E.
0 D.
9 C.
1- B.
9- A.
5312Limit x
+−−∞→
x x
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March 18, 2016 Editor Hendry. P 28
9-5312
Limit
5312
)53()12(Limit
5312
5312x x5312Limit
9x
9x
9x
=
++−
−−
=++−+−−
=++−
++−+−−
→
→
→
x x
x
x x
x x
x x
x x x
#P$#N
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March 18, 2016 Editor Hendry. P 2-
)3)(1(Limit .2
1123Limit .1
x
22
x
x x x
x x x x
−++
+−−+−
∞→
∞→
Lihat Haaan Beri4t
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March 18, 2016 Editor Hendry. P 30
9-limitn/ama%a ,a*i%a 3.
9limitn/ama%a ,a*i%a .2
a2
6- + limitn/ama%a ,a*i%a 1.
ma%a) 6x x +xax(Limit 22x
=<=>
==
+−−++∞→
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March 18, 2016 Editor Hendry. P 31
1 E.
31 D.
0 C.
9 B.
9- A.
1123Limit .1 22x
+−−+−∞→
x x x x
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March 18, 2016 Editor Hendry. P 33
2 E.
1 D.
0 C.
2
1 B.
2
1- A.
...)3)(1(Limitx
=−++∞→
x x x
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March 18, 2016 Editor Hendry. P 3)
22
4
12
0-4
a2
6- +
Limitn/a ma%a ,a $a'na
=
==
=
#P$#N
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March 18, 2016 Editor Hendry. P 3*
)5434x(Limit Hitungla 22x
x x x −−+∞→
3 E.
2 D.
1 C.
0 B.9 A.
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March 18, 2016 Editor Hendry. P 36
2
4
42
)5(3a2
6- +a&alalimitn/ama%a a$a'na
==−−
=
#P$#N
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March 18, 2016 Editor Hendry. P 3+
0 E.
2
1 D.
4
5 C.
54 B.
9 A.
...345)x(4xLimit 2x
=−−+∞→
x
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March 18, 2016 Editor Hendry. P 38
4
5
42
05a2
6- +a&alalimitn/ama%a ,a $a'na
=−
=
#P$#N
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March 18, 2016 Editor Hendry. P 3-
2 E.
1 D.2
1 C.
0 B.
9 A.
...)2x-(xLimit 2x
=−∞→
x
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March 18, 2016 Editor Hendry. P )0
1
2
2
12
20a2
6- +a&alalimitn/ama%a ,a $a'na
==+
=
#P$#N
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March 18, 2016 Editor Hendry. P )1
0g(x)Limit:g(x)Limit
f(x)Limit
g(x)
f(x)Limit .
f(x)Limit%%(f(x))Limit 5.
g(x)Limitf(x).Limitf(x).g(x)Limit 4.
g(x)Limitf(x)Limitg(x)f(x)Limit 3.
af(x)Limitma%ax,f(x)*i%a 2.
f(x)Limitma%a,f(x)*i%a 1.
ax
ax
ax
axax
axaxax
axaxax
ax
ax
≠=
=
=+=+
==
==
→
→
→
→
→→
→→→
→→→
→
→
a x
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March 18, 2016 Editor Hendry. P )2
PENE&APAN E#&EMA L$M$ UAMA
...;
Limit .
...)5(4xLimit +.
...3Limit a.
Hitungla
23x
2
4
2
x
=+
=+
=
→
→
→
x
x
x
x
x
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March 18, 2016 Editor Hendry. P )3
1
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March 18, 2016 Editor Hendry. P ))
[ ][ ] [ ]
4
204
4544
xLimit5Limit4
xLimit5xLimit4
5xLimit4xLimit
)5(4xLimit +.
2
4x
2
4x
4x
2
4x
4x
2
4x
2
4
=
+=
+
+
+
+
=+
→→
→→
→→
→
x
x x
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March 18, 2016 Editor Hendry. P )*
3
;
Limit 1.23x
=
+→
x
x
;LimitxLimit3x
2
3x →→
+
4
3
;3
3
2
=
+
=
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March 18, 2016 Editor Hendry. P )6
[ ]
[ ]f(x).g(x)Limitn
&'ngan'f(x)1Limit 2.
g(x).f(x)Limitm
&'ngan'f(x)1Limit .1
0x
ng(x)
0x
x
mg(x)
x
→
→
∞→
∞→
==+
=
=+
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March 18, 2016 Editor Hendry. P )+
[ ] '1Limit .3
'
1
1limit .2
'
1
1Limit 1.
1
0x
x
x
=+
=
−
=
+
→
−
∞→
∞→
x x
x
x
x
x
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March 18, 2016 Editor Hendry. P )8
' E
' D.' C.
0 B.
'
1 A.
....2
11Limit
2
9n
312
=
−
++++
→
nn
n
n
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March 18, 2016 Editor Hendry. P )-
2
9n
2
2
2
9n
9n
9
m
9n
'2
11Limit *a&i
2m nilai&i'l'
n&i+agi 'n/'+ut&an='m+ilang
32Limitm
3n12n.
2-n1n Limitm
3n
12n g(x) :
2-n
1n f(x)
f(x).g(x)Limitm ana&im,2'2n
1n1Limit
312
=
−
++
=
−+
+=
++
+=
+
+=
+=
==
−
++
→
→
→
→→
++
n
n
nn
nn
nn
nn
#P$#N
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March 18, 2016 Editor Hendry. P *0
2
4
29x
' E.
' D.'
1 C.
1 B.0 A.
....1
1Limit
2
=
+
−
→
x x
x
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March 18, 2016 Editor Hendry. P *1
[ ]
'1
1Limit *a&i
1m
&i&aat&'ngan x&i+agi 'n/'+ut&an='m+ilang
4x Limit4x
x
1 Limitm
*a&i 4xg(x)&anx
1f(x)
f(x).g(x)Limitm&imana'1
1Limit
4
29x
2
2
2
9x
2
29x
2
2
9x
m
4
29x
2
2
=
+
=
−=−
=
−==
==
+
−
→
→→
→
−
→
x x
x x
x
x
x
x
#P$#N
SOAL LATIHAN
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SOAL LATIHAN
March 18, 2016 Editor Hendry. P *2
)1(Limit . )11(Limit .4
)1(Limit .; )3
21(Limit .3
)1(Limit . )2
1
1(Limit .2
)21(Limit .5 )x
1(1Limit 1.
ini +'i%utlimit-LimitHitungla
1
0 x
429 x
1
0 x9 x
2
0 x9x
1
0 x
1x
9x
2 x x x
x x
x x
x
x x
x x
x x
x
−+
−−
−+
++
→−
→
→
−
→
→→
→
+
→
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March 18, 2016 Editor Hendry. P *3
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March 18, 2016 Editor Hendry. P *)
8/19/2019 Limit Fungsi Genap1
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March 18, 2016 Editor Hendry. P **
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March 18, 2016 Editor Hendry. P *6
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March 18, 2016 Editor Hendry. P *+
1 E.
21 D.
0 C.
9 B.
9- A.
.....2x8in
8in xLimit
0x=
→
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March 18, 2016 Editor Hendry. P *8
2
1
2.1
1
x2C
1Limit
xC28in x
8in xLimit
2x8in
8in xLimit
0x
0x0x
=
=
=
=
→
→→
#P$#N
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March 18, 2016 Editor Hendry. P *-
1 E.
21 D.
0 C.
9 B.
9- A.
...8in x
2xC1Limit
0x=−
→
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March 18, 2016 Editor Hendry. P 60
0 08in2
8in x2Limit
8in x
x8in2 Limit
8in x
2xC1Limit
0x
2
0x0x
==
=
=−
→
→→
#P$#N
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March 18, 2016 Editor Hendry. P 61
1 E.
0 D.
1- C.
9 B.
9- A.
...
)
3
(x"an
)3
>(x
Limit3
x=
+
+
−→ π π
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March 18, 2016 Editor Hendry. P 62
1
)3
(x"an
)3
>(x
Limit*a&i
1u"an
ulimit
)3
(x"an
)3
>(x
Limit'ingga
0,uma%a,3-x*i%a3 xu?ial%an
)3
(x"an
)3
>(x
Limit
3
3
3
-x
0u-x
x
=+
+
==+
+
→→+=
+
+
→
→→
−→
π
π
π π
π
π
π
π
#P$#N
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March 18, 2016 Editor Hendry. P 63
g(x)&anf(x)fungintuuna
a&ala(x)@g&an(x)@f (x)@g
(x)@f Limitg(x)
f(x)Limit
8++ H8="ALL@ Dalil
nm'ngguna%a&'nganan&i'l'ai% &aat'+utLimit t'
ma%a,0
0anm'ngail% f(x) a&axnilai%anu+titui%ita i%a
i"ignm'tfungiLimitmauunAla+a,fungiLimitAa+ila
axax →→ =
LOGO
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LOGO
Takut akan Tuhan adalah ermulaanPen!etahuan Amsal " a#at $a
MOTTO SKKK%
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