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ikadub [295]
3 years ago
9

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

Mathematics
2 answers:
zhannawk [14.2K]3 years ago
7 0

\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.

Sophie [7]3 years ago
4 0

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.

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\bf \begin{cases}
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----------\\
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\end{cases}\\\\
-------------------------------\\\\
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\begin{array}{llll}
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