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

`(5x)/(x-2)+(7x)/(x^2+2)=\frac5{1-\frac2x}+\frac{\frac7x}{1+\frac2{x^2}}\to5+0=5`

so the answer is B.

Answer 2

B is correct

The value of limit is 5

Explanation:

We are given a limit
`L=\lim_(x\rightarrow \infty)\left ( (5x)/(x-2)+(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)(5x)/(x-2)+\lim_(x\rightarrow \infty)(7x)/(x^2+2) \right )`

Divide each limit by x at numerator and denominator

`L=\left ( \lim_(x\rightarrow \infty)(5)/(1-2/x)+\lim_(x\rightarrow \infty)(7/x)/(1+2/x^2) \right )`

Apply limit

`L=\left ( (5)/(1-2/\infty)+(7/\infty)/(1+2/\infty) \right )`

`L= (5)/(1-0)+(0)/(1+0)`

`L=5+0`

L=5

Hence, The value of limit is 5