Nilai lim_(x→∞) (4x²−2x)/((x+1)(3−2x)) sama dengan…

Nilai lim_(x→∞) (4x²−2x)/((x+1)(3−2x)) sama dengan…

Jawaban yang benar adalah -2

Jika diketahui:
lim_(x→∞) (a1. x^m + a2. x^(m-1) + a3. x^(m-2) + … )/(b1. x^n + b2. x^(n-1) + b3. x^(n-2) + … )

Nilai limit bentuk di atas, ada 3 kemungkinan, yaitu:
> Jika m = n, maka nilai limit = a1/b1
> jika m > n, maka nilai limit = ∞
> jika m < n, maka nilai limit = 0

Ingat:
(a + b)(c – d) = a.c – a.d + b.c – b.d

Pembahasan,

= lim_(x→∞) (4x² – 2x)/(x + 1)(3 – 2x)
= lim_(x→∞) (4x² – 2x)/(3x – 2x² + 3 – 2x)
= lim_(x→∞) (4x² – 2x)/(-2x² + x + 3)

Karena pangkat tertinggi pada pembilang (m) sama dengan pangkat tertinggi pada penyebut (n), yaitu m = n = 2, maka nilai limitnya yaitu:
= 4/(-2)
= -2

Jadi, nilai limitnya adalah -2

Rekomendasi lainnya :

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