Question

evaluate the limit (lim_{x
ightarrowinfty}\frac{2 + 10x}{6-4x})

Explanation:

Step1: Divide numerator and denominator by highest - power of x

Divide both the numerator and denominator of $\frac{2 + 10x}{6-4x}$ by $x$. We get $\lim_{x
ightarrow\infty}\frac{\frac{2}{x}+ 10}{\frac{6}{x}-4}$.

Step2: Evaluate the limit of each term

As $x
ightarrow\infty$, $\lim_{x
ightarrow\infty}\frac{2}{x}=0$ and $\lim_{x
ightarrow\infty}\frac{6}{x}=0$. So, $\lim_{x
ightarrow\infty}\frac{\frac{2}{x}+ 10}{\frac{6}{x}-4}=\frac{0 + 10}{0-4}$.

Step3: Simplify the result

$\frac{0 + 10}{0-4}=-\frac{10}{4}=-\frac{5}{2}$.

Answer:

$-\frac{5}{2}$