sifat limit fungsi aljabar dan contoh soal
TRANSCRIPT
OLEH:
ASRIFIDA JUWITA TANJUNG
“SIFAT – SIFAT LIMIT FUNGSI ALJABAR”
Sifat-Sifat Limit Fungsi:
1). lim k = k ,untuk k adalah bilangan realx a
2). lim x = a x a
3). lim kf(x) = k.lim f(x)x a x a
4). lim [f(x) + g(x)] = lim f(x) + lim g(x)x a x a x a
5). lim [f(x) – g(x)] = lim f(x) – lim g(x)x a x a x a
6). lim [f(x).g(x)] = lim f(x) . lim g(x)x a x a x a
7). lim = x a
8). lim =x a
9). lim = x a
Contoh Soal
1). Hitunglah nilai lim (7x-4)x 2
Jawab
lim (7x-4) = lim 7x – lim 4
x 2 x 2 x 2
7 (2) - 4 = 7 lim x – 4 x 2
14 - 4 = 7 lim 2 - 4
x 2
= 7 . 2 – 4= 14 – 4 =
Teorema 5lim [f(x) – g(x)] = lim f(x) – lim g(x)
x a
Teorema 1lim k = kx a
Teorema 2lim x = ax a10
10
2). Tentukan limx 2
Jawab:
lim =
x 2
=
=
=
= = = =
Teorema 7
lim =x a
Teorema 5lim [f(x) – g(x)] = lim f(x) –
lim g(x) x a
Teorema 1lim k = kx a
Teorema 2lim x = ax a
3). Tentukan limx 3
Jawab:
lim =
x 3
=
=
=
=
= = =
Teorema 9lim =x a
Teorema 5lim [f(x) – g(x)] = lim f(x) –
lim g(x) x a
Teorema 1lim k = kx a
Teorema 2lim x = ax a
4
4
4). Tentukan limx 3
Jawab:
lim =
x 3
=
=
=
=
= =
Teorema 8lim =x a
Teorema 4lim [f(x) + g(x)] = lim f(x) + lim g(x)x a x a x a
Teorema 1lim k = kx a
Teorema 2lim x = ax a
49 49
5). Tentukan lim 2(4x-1)x 3
Jawab:
lim 2(4x-1) = 2 lim 4x -1
x 3 x 3
2 (4.3 – 1) = 2 (lim 4x – lim 1)x 3 x 3
2 (12 – 1) = 2 (4 lim x – 1)x 3
2 (11) = 2 (4 lim 3 – 1)
x 3
= 2 (4.3 – 1)
= 2 (12 – 1) = 2 ( 11) =
Teorema 3lim kf(x) = k.lim f(x)x a x a
Teorema 5lim [f(x) – g(x)] = lim f(x) –
lim g(x) x a
Teorema 1lim k = kx a
Teorema 2lim x = ax a
22
22
6). Tentukan lim 2x . 4xx 1
Jawab:
lim 2x . 4x = lim 2x . lim 4x
x 1 x 1 x 1
2 (1) . 4(1) = 2 lim x . 4 lim xx 1 x 1
2 . 4 = 2 lim 1 . 4 lim 1
x 1 x 1
= 2 . `1 . 4 . 1
=
Teorema 6
lim [f(x).g(x)] = lim f(x) .
lim g(x)x a x a x a
Teorema 2lim x = ax a
Teorema 1lim k = kx a
8
8