Question

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

Answer 1

$\dfrac{4x}{x-5}=\dfrac4{1-\frac5x}$, and as $x\to\infty$, the $\dfrac5x$ term vanishes.

$\dfrac{4x}{x^2+5}=\dfrac{\frac4x}{1+\frac5{x^2}}$, and as $x\to\infty$, both $\dfrac4x$ and $\dfrac5{x^2}$ vanish.

So

$\displaystyle\lim_{x\to\infty}\left(\frac{4x}{x-5}+\frac{4x}{x^2+5}\right)=\lim_{x\to\infty}(4+0)=4$

and the answer is C.

Answer 2

Answer:

Option C. 4 is the correct option.

Step-by-step explanation:

The given expression is $\lim_{x\rightarrow \oe }[\frac{4x}{x-5}+\frac{4x}{x^{2}+5}]$

We have to calculate the limit of the given expression.

Now we will convert the equation in the form as given below

$=\lim_{x\rightarrow \oe }[\frac{4}{1-\frac{5}{x}}+\frac{4}{x+\frac{5}{x}}]$

We have done this transformation of the equation because we know

$\lim_{x\rightarrow \oe }[\frac{1}{x}]=0$

Now by the property of limit second term in the question will be vanished

and the remaining part will be

$\lim_{x\rightarrow \oe }[\frac{4}{1-\frac{5}{x}}]$

Now by putting x→∞ we get

$[\frac{4}{1-0}]=4$

Therefore option C is the correct answer.