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
lilavasa [31]
3 years ago
7

"TexFormula1" title="\sf \lim_{x \to \infty} \cfrac{\sqrt{x-1}-2x }{x-7}" alt="\sf \lim_{x \to \infty} \cfrac{\sqrt{x-1}-2x }{x-7}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
BARSIC [14]3 years ago
5 0
<h3>Answer:  -2</h3>

======================================================

Work Shown:

\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}\left(\sqrt{x-1}-2x\right) }{ \frac{1}{x}\left(x-7\right) }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}*\sqrt{x-1}-\frac{1}{x}*2x }{ \frac{1}{x}*x-\frac{1}{x}*7 }\\\\\\

\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}}*\sqrt{x-1}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}*(x-1)}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x}-\frac{1}{x^2}}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \frac{ \sqrt{0-0}-2 }{ 1-0 }\\\\\\\displaystyle L = \frac{-2}{1}\\\\\\\displaystyle L = -2\\\\\\

-------------------

Explanation:

In the second step, I multiplied top and bottom by 1/x. This divides every term by x. Doing this leaves us with various inner fractions that have the variable in the denominator. Those inner fractions approach 0 as x approaches infinity.

I'm using the rule that

\displaystyle \lim_{x\to\infty} \frac{1}{x^k} = 0\\\\\\

where k is some positive real number constant.

Using that rule will simplify the expression greatly to leave us with -2/1 or simply -2 as the answer.

In a sense, the leading terms of the numerator and denominator are -2x and x respectively. They are the largest terms for each, so to speak. As x gets larger, the influence that -2x and x have will greatly diminish the influence of the other terms.

This effectively means,

\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 } = \lim_{x\to\infty} \frac{ -2x }{ x} = -2\\\\\\

I recommend making a table of values to see what's going on. Or you can graph the given function to see that it slowly approaches y = -2. Keep in mind that it won't actually reach y = -2 itself.

You might be interested in
.Sally is comparing 2 types of house insurance. Both companies provide the same service; however,
Nostrana [21]

Answer:

car help

Step-by-step explanation:

In order to determine which type of house insurance would be considered as cheapest first it is necessary to determine either monthly or either weekly

As we know that

Generally in the month there is a 4 weeks

So For Car Help, the monthly would be

= $8.60 × 4

= $34.40

And for Car safety, the quoted price is $36.10 per week

So according to the above calculation the car help would be choose as the cheapest

6 0
3 years ago
.The table shows the relationship between the number of hours and pages read by Melissa. What is the constant of proportionality
stepan [7]
Can you show the table
If the line is going down then it’s negative I was going up it’s positive if the line is constant it’s a constant
The more hours that she read the more pages that she’s able to read
8 0
3 years ago
Divide the polynomial (x^2 + 3x + 5) by 2x + 1​
umka21 [38]

Answer:

50888888888888888888+++++

7 0
3 years ago
Please Answer!!!!
kykrilka [37]

Answer:

Its A

Step-by-step explanation:

Sorry I don't have time but it is A I had this before

3 0
3 years ago
Read 2 more answers
Given the figure, if ∠ABC is 20° and C is the center of the circle, what is the measure of the central angle ∠ACB? A) 40° B) 70°
kramer

Answer:

D) 140°

Step-by-step explanation:

The total number of degrees in a triangle is 180. Since both sides of the triangle are the radius of the circle, the triangle is isosceles. Therefore the two opposite angles are equal. Thus, the central angle is 180° − 2(20°) = 140°.

7 0
3 years ago
Read 2 more answers
Other questions:
  • Using the graph, determine the value of the slope.<br> What is the slope?
    8·2 answers
  • What is 2.23 as a fraction
    14·2 answers
  • What’s 6 times 6 divided by 2 plus 2
    12·2 answers
  • What is two plus two​
    7·2 answers
  • If the vertex of a parabola is (-8,-6), what is the axis of symmetry
    12·1 answer
  • 285.39154 to the nearest hundredth
    8·2 answers
  • Where are the zeros for f(x) = 3 sin 2x on the interval [0, 21)?
    15·1 answer
  • An employee earns a gross pay of $1,200.00 per week. The employee's net pay is $850.00. The employee's voluntary 401(k) contribu
    7·1 answer
  • Simplify.<br> [(63 = 18)2 – 8] * 5<br> 136<br> O 680<br> 0-39<br> -35
    9·1 answer
  • 2(x -9) = 9 divided ( - 1/3) what value of x makes the equation true <br> plsss help :)))
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!