Question

12 mark for review what is lim(x→∞) (x - 4)/(2 + x - 4x²)? a -2 b -1/4 c 1/2 d 1

Explanation:

Step1: Divide by highest - power term

Divide both the numerator and denominator by $x^{2}$. We get $\lim_{x
ightarrow\infty}\frac{\frac{x^{2}}{x^{2}}-\frac{4}{x^{2}}}{\frac{2}{x^{2}}+\frac{x}{x^{2}} - 4}=\lim_{x
ightarrow\infty}\frac{1-\frac{4}{x^{2}}}{\frac{2}{x^{2}}+\frac{1}{x}-4}$.

Step2: Apply limit rules

As $x
ightarrow\infty$, $\lim_{x
ightarrow\infty}\frac{1}{x}=0$ and $\lim_{x
ightarrow\infty}\frac{1}{x^{2}} = 0$. So, $\lim_{x
ightarrow\infty}\frac{1-\frac{4}{x^{2}}}{\frac{2}{x^{2}}+\frac{1}{x}-4}=\frac{1 - 0}{0 + 0-4}$.

Step3: Simplify the result

$\frac{1-0}{0 + 0 - 4}=-\frac{1}{4}$.

Answer:

B. $-\frac{1}{4}$