Nilai dari limx→2x3−4xx−2=…

Nilai dari $\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\dots$

A. 32

B. 16

C. 8

D. 4

E. 2

Jawab

cara substitusi

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\frac{2^3-4(2)}{2-2}$

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\frac{8-8}{0}$

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\frac{0}{0}$

karena hasil dari cara substitusi adalah $\frac{0}{0}$ maka harus cari cara yang lain

cara faktor

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\frac{x(x^2-4)}{x-2}$

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\underset{x\to 2}{lim}x\times \underset{x\to 2}{lim}\frac{x^2-4}{x-2}$

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\underset{x\to 2}{lim}x\times \underset{x\to 2}{lim}\frac{\cancel{(x-2)}(x+2)}{\cancel{x-2}}$

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\underset{x\to 2}{lim}x\times \underset{x\to 2}{lim}(x+2)$

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=\underset{x\to 2}{lim}2\times \underset{x\to 2}{lim}(2+2)$

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=2\times 4$

$\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=8$

Kesimpulan

Jadi, nIlai $\underset{x\to 2}{lim}\frac{x^3-4x}{x-2}=8$

Jaawaban: D

Muda Berkarya Intelektual Normatif

Muda Berkarya Intelektual Normatif