Use calculus to evaluate (lhopitals rule)
lim x>infinity x^2 - ln(2/x)/3x^2 + 2x

Answers

Answer 1

Answer:

1/3

Step-by-step explanation:

[tex][x^2 - ln(2/x)]/[3x^2 + 2x]\\[/tex]

∞/∞

[tex]\frac{d}{dx}[x^2-ln(2/x)] =2x+\frac{1}{x}\\ \frac{d}{dx}[3x^2+2x]=6x+2\\\frac{2x+\frac{1}{x}}{6x+2}[/tex]

Also ∞/∞

[tex]\frac{d}{dx}[2x+\frac{1}{x}]=2-1/x^2\\\frac{d}{dx}[6x+2]=6\\\\[/tex]

[tex]\lim_{x \to \infty} \frac{2-\frac{1}{x^2} }{6}\\=\frac{2}{6} \\=\frac{1}{3}[/tex]


Related Questions

the speed of the current in a creek is 2 mph. A person can kayak 4 mi upstream in the same time that it takes him to kayak 8 mi downstream. What is the speed of the persons kayak in still water?

Answers

Answer:

I think 6 mph

Step-by-step explanation:

I needore characters so ingnor this sentence.

Can someone please help me I’m it’s kinda blurry but you have to zoom in

Answers

Answer:

1 is x=53

2 is x=37

3 is x=45

4 is x=180

5 is x=130

6 is x=90

7 is x=15

8 is x=60

9 is x=20

10 is x=140

11 is x=47

12 is x=18

Step-by-step explanation: These can all be solved using vertical angles, complimentary angle theorem, and supplementary angle theorem! Really fancy names to say that opposite angles are equal, vertical angles (like #5).  Two angles that add up to 180 degrees forming a straight line, complimentary angles (like in #1). And in a right angle two angles will always add up to 90 degrees (#7 for example). 10 11 and 12 require you to use vertical angles and complimentary angles to solve them.

above ^^^^^^^^^^^^^^^^^^^^^^^

Simplify the expression 1/2(h+4) - 1/8(h+4) by combining like terms.
A. 1/6 (h+4)
B. 3h/8 + 2/10
C. 3/8 (h-4)
D. 3/8 (h+4)
WILL GIVE BRAINLIEST IF THE ANSWER IS CORRECT.

Answers

Answer:

3h/8+3/2

Step-by-step explanation:

Answer:

D. should be the correct answer.

An insurance company divides its policy holders into three categories: low risk, moderate risk, and high risk. The low-risk policy holders account for 55% of the total number of people insured by the company. The moderate-risk policy holders account for 25%, and the high-risk policy holders account for 20%. The probabilities that a low-risk, moderate-risk, and high-risk policy holder will file a claim within a given year are respectively 5%, 15% and 60%. Given that a policy holder files a claim this year, what is the probability that the person is a moderate-risk policy holder?

Answers

Answer:

0.2027 = 20.27% probability that the person is a moderate-risk policy holder

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Policy holder files a claim.

Event B: The person is a moderate-risk policy holder.

Probability of filling a claim:

5% of 55%(low risk)

15% of 25%(moderate risk)

60% of 20%(high risk).

So

[tex]P(A) = 0.05*0.55 + 0.15*0.25 + 0.6*0.2 = 0.185[/tex]

Files a claim and is moderate risk:

15% of 25%(moderate risk)

So

[tex]P(A \cap B) = 0.15*0.25 = 0.0375[/tex]

Given that a policy holder files a claim this year, what is the probability that the person is a moderate-risk policy holder?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0375}{0.185} = 0.2027[/tex]

0.2027 = 20.27% probability that the person is a moderate-risk policy holder

Your test scores in one class are 79 and 83. What possible scores can you earn on your next test to have a test average between 81 and 87, inclusive?

Answers

Answer:

83 and 84

Step-by-step explanation:

these numbers will both work because if you make an equation 79+83+x=y, with 87≥y≥81, and plug in these numbers for x, the answers are around 82 which is within the range.

Help me me please now

Answers

Answer:

AAA

Step-by-step explanation:

The AAA (angle-angle-angle) theorem proves they have 3 congruent angles, but not congruent sides.

my question is in the picture​

Answers

Answer:

x = 1

y = -1

Step-by-step explanation:

-5x + 5y = -10

rewrite the order:

5y = 5x  - 10

6x + 5y = 1

rewrite the order:

5y = 1 - 6x

substitute for 5y:

5x - 10 = 1 - 6x

simplify:

11x = 11

x = 1

5y = 1 - 6(1) = -5

y = -1

Please help i will give branliest!!!

Answers

Answer:b

Step-by-step explanation:

3.5*5*.5=8.75

2. In triangle ABC, SA is a right angle, and m B = 45°
(1 point)
C
16 ft
A
B.
What is the length of BC? If your answer is not an integer, leave it in simplest radical form.
O 16 ft
O 16.2 ft
O 16.5 ft
O 32 ft

Answers

Answer:

[tex]16\sqrt{2}[/tex]

Step-by-step explanation:

The given triangle shown is a 45-45-90. We can use this picture attached to figure out BC.

n in this case is 16ft

Based on the picture, we can get BC's length, which is n[tex]\sqrt{2}[/tex]

BC = [tex]16\sqrt{2}[/tex]

Can you help with this I don’t know how to solve this.

Answers

Answer:

[tex]arclength = 13.44 ft[/tex]

Step-by-step explanation:

We are given PS = 28 feet, which is the length of the diameter.

The formula for arc length is  [tex]2\pi r\frac{x}{360}[/tex], where x is the degrees.

So, we need to find the radius. We know that the radius is half of the diameter, so:

[tex]\frac{28}{2}=14 ft[/tex]

We also need to find ∠TXS. Since we know the diameter is a line that crosses the center point of the circle, we also know that ∠PXT and ∠TXS add up to 180°. So:

∠PXT + ∠TXS = 180

125 + ∠TXS = 180

∠TXS = 180 - 125

∠TXS = 55°

Now, we can use the arc length formula:

[tex]arclength=2\pi r\frac{x}{360}[/tex]

[tex]arclength=2\pi (14)\frac{55}{360}[/tex]

[tex]arclength=13.43903524...[/tex]

[tex]arclength = 13.44 ft[/tex]

Check my work to make sure! Hope this helps!

An English professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 61% C: Scores below the top 39% and above the bottom 20% D: Scores below the top 80% and above the bottom 10% F: Bottom 10% of scores Scores on the test are normally distributed with a mean of 72.8 and a standard deviation of 7.3. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answers

Solution :

The test is distributed normally with mean of 72.8 and the standard deviation of 7.3

Finding numerical limits for the D grade.

D grade : Scores below the top 80% and above the bottom 10%.

Let the bottom limit for D grade be [tex]$D_1$[/tex] and the top limit for D grade be [tex]$D_2$[/tex].

First find the bottom numerical limit for a D grade is :

[tex]$P(X<D_1)= 0.10$[/tex]

[tex]$P(X\leq D_1)= 0.10$[/tex]

[tex]$P\left(\frac{X-\mu}{\sigma} \leq \frac{D_1-\mu}{\sigma}\right) = 0.10$[/tex]

[tex]$P\left(Z \leq \frac{D_1-72.8}{7.3}\right) = 0.10$[/tex]    ..........(1)

From (1)

[tex]$\frac{D_1 - 72.8}{7.3} = -1.28$[/tex]

[tex]$D_1 = -1.28(7.3)+72.8$[/tex]

      = 63.45

       ≈ 64

Now the top numerical limit for D grade :

[tex]$P(X>D_2)= 0.80$[/tex]

[tex]$1-P(X\leq D_2)= 0.80$[/tex]

[tex]$P(X\leq D_2)= 1-0.80$[/tex]

[tex]$P(X\leq D_2)= 0.20$[/tex]

[tex]$P\left(\frac{X-\mu}{\sigma} \leq \frac{D_2-\mu}{\sigma}\right) = 0.20$[/tex]

[tex]$P\left(Z \leq \frac{D_2-72.8}{7.3}\right) = 0.20$[/tex]    ..........(2)

From (2)

[tex]$\frac{D_2- 72.8}{7.3} = -0.84$[/tex]

[tex]$D_12= -0.84(7.3)+72.8$[/tex]

      = 66.668

       ≈ 67

Therefore, the numerical limit for a D grade is 64 to 67.

Which one is a unit rate?
sk
5 pounds in 2 bags
15 miles per gallon
$8.00 for 3 boxes of oranges
22gallons of water in 5 days

Answers

number 2- 15 miles per gallon.
the key word in this example is per, which is a key word for unit rate.
hope this helps:)

Write an equation to represent the total cost y for x days of renting a mid-size car from each of these companies. *

Answers

Answer:

Step-by-step explanation:

Hindi ko alm hehe

Yo no si sorryyyyyyyyyyyyyyyyyyyyyyy

Is the sum of the
angle measures always equal to the
sum of the arc measures


Yes or no ?

Answers

Answer
Yes


Explanation
I just know

find the value of b in rectangle

Answers

be will equal 23. i’ll attach work

SO BAD RN SMH SMH...HELP ME WITH MATH
4 x 2 - 5 + 63 + 1 =

Answers

Answer:

67

Step-by-step explanation:

4x2= 8-5= 3 + 63 = 66 + 1 = 67

Help ?? Anyone and how

Answers

Answer:

just insert the x numbers in the calculation.. so for x = - 3 - > (- 3) / 2 +4 = 2.5

Step-by-step explanation:

x - 2 = y 3

and so on

what is 1+1? pls, I need help. its for school

Answers

Answer:

its 2 :)

Step-by-step explanation:

Answer:

oh what a stiff XD

Step-by-step explanation:

ok 1+1=2 lol ❤️✌️ hey where you from I'm anmol kulkar from India

Corrie breathed 1 × 10^7 times in a year. She blinked 8 × 10^6 times that year. How many more times did Corrie breathe in a year than she blinked in that year? Write your answer in standard notation

Answers

Snskskskjssksj28828384838188:$2&82:&/&:&

Step-by-step explanation:

1 × 10 ^7 - 8 × 10 ^ 6

2 × 10 ^ 6 which is also equivalent to 2,000,000

The difference between one-third of a number and 11 is 10 in number form

Answers

1/3n - 11 = 10
1/3n = 21
n= 21x 3
n = 63

Answer:

63

Step-by-step explanation:

The difference between one-third of a number and 11 is 10. x = 3*21, x = 63.

#5
(10 pts) You are jumping on a trampoline. For one jump, your height y (in feet) above the trampoline after t seconds can
be represented by y = -16t² + 24t. How many seconds are you in the air?

Answers

Answer:

1.5 seconds

Step-by-step explanation:

i took a test with the same question

Answer:

1.5

Step-by-step explanation:

taking the test

m∠IJK=155° and m∠ZJK=35°. Find m/∠IJZ

Answers

120° because 155-35=120 since IJZ is inside the IJK so you would have to subtract the ZJK from the IJZ.

I am 20 years older than twice my daughter's age how old is my daughter you should already know my age in the last problem
17 years ago I was half the age I am now how old am I
this question is 100 points

Answers

Answer:

You are 34 years old

Step-by-step explanation:

Because, 34-17=17

17 is half of 34.

2x+20=y

y-17=0.5y

+17    +17

y=0.5y+17

2(0.5y+17)+20=0.5y+17

y+34+20=0.5y+17

y+54=0.5y+17

y=34

Answer:

Step-by-step explanation:

x= "I" age

x is 20 years older than x's daughter's age.

To find out daughter's age = 17x2 (34)

34-20 = 14

The daughter is 14.

Determine the equivalent system for the given system of equations.


4x − 5y = 2

10x − 21y = 10


A. 4x − 5y = 2

3x − y = 4

B. 4x − 5y = 2

24x − 47y = 22

C. 4x − 5y = 2

10x + 3y = 15

D. 4x − 5y = 2

14x + 26y = 12

Answers

Answer:

B) 4x − 5y = 2

24x − 47y = 22

Express as a difference: a+b, a+5

Answers

Answer:

a - (-b), a - (-5)

Step-by-step explanation:

A double negative negative is a positive, so a - (-b) = a + b, and a - (-5) is a + 5. However, a double negative is still a difference, so this answer works.

Answer:

The answer is a-(-b)

Step-by-step explanation:

It says difference, so you delete plus sign with minus sign

You have different lengths of material to use for a craft project:

0.93m 1.24m 0.62m 3.41m 1.5m 1.4m

Convert each length to centimetres, and then add them together to correctly calculate the total length.

Answers

Answer:

[tex]Lengths: 93cm, 124cm, 62cm, 341cm, 150cm, 140cm[/tex]

[tex]Total := 910cm[/tex]

Step-by-step explanation:

Given

[tex]Lengths: 0.93m, 1.24m, 0.62m, 3.41m, 1.5m, 1.4m[/tex]

Required

Convert to length and calculate the total

To calculate to centimeters, we simply multiply each length to 100.

So, we have:

[tex]Lengths: 0.93m, 1.24m, 0.62m, 3.41m, 1.5m, 1.4m) * 100[/tex]

[tex]Lengths: 93cm, 124cm, 62cm, 341cm, 150cm, 140cm[/tex]

The total is:

[tex]Total := 93cm+ 124cm+ 62cm+ 341cm+ 150cm+ 140cm[/tex]

[tex]Total := 910cm[/tex]

how do u find the angle measure of l

Answers

Answer:

The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree.

A kite is shown below with given dimensions in inches. What is the area in square units

Answers

Answer:

320

80

Step-by-step explanation:

Use the multiplier method to decrease £56 by 14% show your working

Answers

Answer: £46.44

Step-by-step explanation:

£56 × 0.86 or (1 - 0.14)

math HELPPP MEEEEEEEE

Answers

Answer : 51x +26y+17

Step-by-step explanation :

Answer: I HAVE YOUR ANSWER!!!!!

Step-by-step explanation:

51x + 26y + 17

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