Question

use the properties of limits to help decide whether the limit exists. if the limit exists, find its value. $lim_{x
ightarrowinfty}\frac{6x}{4x - 6}$ select the correct choice below and, if necessary, fill in the answer box within your choice. a. $lim_{x
ightarrowinfty}\frac{6x}{4x - 6}=square$ (simplify your answer. type an integer or a fraction.) b. the limit does not exist and is neither $infty$ nor $-infty$.

Explanation:

Step1: Divide numerator and denominator by x

$\lim_{x
ightarrow\infty}\frac{6x/x}{(4x - 6)/x}=\lim_{x
ightarrow\infty}\frac{6}{4-\frac{6}{x}}$

Step2: Evaluate limit as x approaches infinity

As $x
ightarrow\infty$, $\frac{6}{x}
ightarrow0$. So $\lim_{x
ightarrow\infty}\frac{6}{4-\frac{6}{x}}=\frac{6}{4 - 0}=\frac{3}{2}$

Answer:

A. $\lim_{x
ightarrow\infty}\frac{6x}{4x - 6}=\frac{3}{2}$