lim f(x) x→∞ if f(x)=8x³ - 8 / 4x³ - 2, find the value of the following limit. 8 +∞ 4 2

Explanation:

Step1: Divide numerator and denominator by $x^{3}$

$\lim_{x\rightarrow\infty}\frac{8x^{3}-8}{4x^{3}-2}=\lim_{x\rightarrow\infty}\frac{\frac{8x^{3}}{x^{3}}-\frac{8}{x^{3}}}{\frac{4x^{3}}{x^{3}}-\frac{2}{x^{3}}}$

Step2: Evaluate the limit of each term

As $x\rightarrow\infty$, $\lim_{x\rightarrow\infty}\frac{8}{x^{3}} = 0$ and $\lim_{x\rightarrow\infty}\frac{2}{x^{3}}=0$. So we have $\frac{\lim_{x\rightarrow\infty}8-\lim_{x\rightarrow\infty}\frac{8}{x^{3}}}{\lim_{x\rightarrow\infty}4-\lim_{x\rightarrow\infty}\frac{2}{x^{3}}}=\frac{8 - 0}{4-0}$

Step3: Simplify the fraction

$\frac{8}{4}=2$

Answer:

2