1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Math:
Dahasolnce [82]

Answer:

a) x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}, x_{2} = \frac{5\pi}{6}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}, b) x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}, x_{2} = \frac{5\pi}{3}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}

Step-by-step explanation:

a) The equation must be rearranged into a form with one fundamental trigonometric function first:

\sqrt{3}\cdot \csc x - 2 = 0

\sqrt{3} \cdot \left(\frac{1}{\sin x} \right) - 2 = 0

\sqrt{3} - 2\cdot \sin x = 0

\sin x = \frac{\sqrt{3}}{2}

x = \sin^{-1} \frac{\sqrt{3}}{2}

Value of x is contained in the following sets of solutions:

x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}

x_{2} = \frac{5\pi}{6}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}

b) The equation must be simplified first:

\cos x + 1 = - \cos x

2\cdot \cos x = -1

\cos x = -\frac{1}{2}

x = \cos^{-1} \left(-\frac{1}{2} \right)

Value of x is contained in the following sets of solutions:

x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}

x_{2} = \frac{5\pi}{3}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}

7 0
3 years ago
67 and 113 that is multiple of 4,5 and 8
MA_775_DIABLO [31]

Answer:

No, 67 and 113 are not multiples of 4,5 and 8

Step-by-step explanation:

6 0
4 years ago
Determine whether the lines are parallel, perpendicular, or neither. <br> x = 3<br> and y = 4
Katyanochek1 [597]
I think they’re perpendicular lines
5 0
3 years ago
How do you write 22 1/3 as a fraction
Sergeeva-Olga [200]
Well, first you multiply 22×3 and then add the answer by 3!. whole times denominator plus numerator!
5 0
4 years ago
Read 2 more answers
Please help me with these questions.
Debora [2.8K]
4. k less than 3.5, so a number k is being taken away from 3.5:
The answer is 3.5-k

5. the sum of g and h, reduced by 11, so you need a set of parentheses to write this one: (g+h)-11

6. 5 less than y, plus g, so do a combination of the strategies used in the previous two problems and you will get: (y-5)+g

7. 5 less than the sum of y and g, you are taking away 5 from the sum of two numbers, y and g, so: (y+g)-5

Hope this helps :-)
5 0
3 years ago
Other questions:
  • Find the least common denominator of -7/x and -5/6x^2
    11·1 answer
  • How much is 19.5% of 600? Round the answer to the nearest whole number.
    6·1 answer
  • Which of the following expressions represents the GCF of 91x 2 y and 104xy 3?
    5·2 answers
  • Xiao's teacher asked him to rewrite the sum 60+90 as the product of the GCF of the two numbers and a sum. Xiao's wrote 3(20 + 30
    7·1 answer
  • What’s is the cubic feet of 24 by 72 by 18
    5·1 answer
  • Find the distance between the following points (-2,4) (3,2)
    7·1 answer
  • Solve: c-10+3c&lt;2 step by step
    12·1 answer
  • Bags of flour come in 3 sizes:
    13·1 answer
  • The population of Arizona in 1970 was 1775 thousand. In 1992 this number had
    8·1 answer
  • Girlcome 5324611502 <br>p:1234​
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!