Question

Use the properties of limits to find the limit.
Picture below

Answer 1

Virtually the same as the last question of yours that I answered. Here we have

$\dfrac{5x}{x-2}+\dfrac{7x}{x^2+2}=\dfrac5{1-\frac2x}+\dfrac{\frac7x}{1+\frac2{x^2}}\to5+0=5$

so the answer is B.

Answer 2

Answer:

B is correct

The value of limit is 5

Step-by-step explanation:

We are given a limit $L=\lim_{x\rightarrow \infty}\left ( \dfrac{5x}{x-2}+\dfrac{7x}{x^2+2} \right )$

Here we need to find value of limit using limit property.

First we distribute limit

$L=\left ( \lim_{x\rightarrow \infty}\dfrac{5x}{x-2}+\lim_{x\rightarrow \infty}\dfrac{7x}{x^2+2} \right )$

Divide each limit by x at numerator and denominator

$L=\left ( \lim_{x\rightarrow \infty}\dfrac{5}{1-2/x}+\lim_{x\rightarrow \infty}\dfrac{7/x}{1+2/x^2} \right )$

Apply limit

$L=\left ( \dfrac{5}{1-2/\infty}+\dfrac{7/\infty}{1+2/\infty} \right )$

$L= \dfrac{5}{1-0}+\dfrac{0}{1+0}$

$L=5+0$

L=5

Hence, The value of limit is 5