limit fungsi · web viewa. limit fungsi aljabar jika author taufikurrahman created date 10/21/2015...
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LIMIT FUNGSI
A. Limit fungsi aljabar
Jika
f (a )g (a )
=00 , maka
limx→a
f ( x )g ( x ) diselesaikan dengan cara sebagai berikut:
1. Difaktorkan, jika f(x) dan g(x) bisa difaktorkan
2. Dikalikan dengan sekawan pembilang atau penyebut jika f(x) atau g(x) berbentuk akar
3. Menggunakan dalil L’Hospital jika f(x) dan g(x) bisa di turunkan
limx→a
f ( x )g ( x )
=f ' (a )g ' (a)
Cara Cepat
1) limx→a
bxc−√dx+e
.= (
b−d )×2⋅c
1.
2) limx→a
b−√cx+dex−f
.= (
−ce )× 1
2⋅b.
3)
limx→0
dx√ax+b−√cx+b
.= ( 2d√ba−c )
4) limx→0
√ax+b−√cx+bdx
.= ( a−c2d√b )
B. Limit fungsi trigonometri
1.limx→0
sin axbx
= limx→0
axsinbx
=ab
2.limx→0
tan axbx
=limx→0
axtan bx
=ab
3.limx→0
sin ax tan bxpx sin cx
= a .bp .c
4.limx→0
1−cosaxbx tan cx
= a2
2bc
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Catatan
Identitas trigonometri yang biasa digunakan
a. 1 – cos A = )(sin2 212 A
b.
1sin x = csc x
c.
1cos x = secan x
d. cos A – cos B = – 2 sin 12 (A + B) sin
12 (A – B)
e. cos A sin B = ½{sin(A + B) – sin(A – B)}
Limit Mendekati Tak Berhingga
1.limx→∞
axn+bxn−1+ .. .cxm+dxm−1+ .. . = p , dimana:
a. p =
ac , jika m = n
b. p = 0, jika n < mc. p = , jika n > m
2.limx→∞
(√ax+b±√cx+d )= q, dimana:
a. q = , bila a > cb. q = 0, bila a = cc. q = –, bila a < c
3.limx→∞
(√ax2+bx+c−√ax 2+qx+r )=b−q2√a
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