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

Please help when Kevin bought a new office phone, he borrowed $1,200 at a rate of 18% for 9 years

Answers

Answer:

where is the rest of the questions

Please help!
Given the figure is a square, find x, y and z

Answers

Answer:

Step-by-step explanation:

Did u find it? Because I can’t figure it out euther

3/5x2/3 thanks for the help

Answers

3   x   2         6

--        --    =   --

5        3         15

6/15 can be simplified to 2/5.

---

hope it helps

The Booster Club sells meals at basketball games . Each meal comes with a choice of a main: hamburgers , pizza , hot dogs, cheeseburgers , or tacos, and a choice of a drink: root beer, lemonade, milk, coffee, tea, or cola. How many possible sandwich/drink combinations are there? (Show work) (2 pts)

Answers

30 combinations is the answer.

Step-by-step explanation:

Each meal comes with a choice of hamburgers, pizza, hot dogs , cheeseburgers or tacos means 5 options.

And a choice of root beer lemonade, milk , coffee, tea or cola means 6 options.

So, possible combination can be =  combinations.

how many 8ths are in a pound

Answers

Answer:There are 129 eighths in one pound of

Step-by-step explanation:


15 * 3/5


14. Will the product be greater than 15?

Answers

Answer:

No

Step-by-step explanation:

When you divide by a fraction or a decimal you are essentially multiplying that by something lesser than one and so the Calculator, if you are using a Calculator to solve this will, see multiplying something by a decimal or a fraction as a division and vice versa.

Which graph represents-5x+4y≥-1?

Answers

Answer:

D!

Step-by-step explanation:

Desmos has a free graphing calculator for future references :)

10 points!! Will mark brainliest. No question just tell me more about Area of Composite Figures and how to find it. I will report If answer is unrelated.

Answers

Answer:

To find the area of a composite figure, separate the figure into simpler shapes whose area can be found. Then add the areas together. Be sure than none of the simpler figures have overlapping areas. To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. This is the same as saying length2 or length squared.

What is the conjugate of (x2-6)?

Answers

Answer:

2(x - 3)

Step-by-step explanation:

For a rhombus, which of the following statements are true? (select all that apply)

1)Opposite sides are parallel
2)All sides are congruent
3)Consecutive angles are congruent
4)Consecutive angles are supplementary
5)All angles are congruent
6)Opposite angles are congruent

Answers

Answer: 1,4,6

Step-by-step explanation:

https://quizlet.com/483245104/geometry-parallelogram-quiz-flash-cards/

American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The league believes that replacing the pitcher, traditionally a weak hitter, with another player in the batting order produces more runs and generates more interest among fans. Below are the average numbers of runs score in American League and National League stadiums for the first half of the 2001 season. **American:** 11.1, 10.8, 10.8, 10.3, 10.3, 10.1,10.0, 9.5, 9.4, 9.3, 9.2, 9.2, 9.0, 8.3 **National:** 14.0, 11.6, 10.4, 10.3, 10.2, 9.5, 9.5, 9.5, 9.5, 9.1, 8.8, 8.4, 8.3, 8.2, 8.1, 7.9 (a) Create two box plots to display this data and comment on what you see. (b) Estimate the mean number of runs scored in American League games with a 95% CI. What concerns do you have about making a similar CI for National League games

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

**American:**

11.1, 10.8, 10.8, 10.3, 10.3, 10.1,10.0, 9.5, 9.4, 9.3, 9.2, 9.2, 9.0, 8.3

**National:**

14.0, 11.6, 10.4, 10.3, 10.2, 9.5, 9.5, 9.5, 9.5, 9.1, 8.8, 8.4, 8.3, 8.2, 8.1, 7.9

Kindly view attached picture for boxplot :

Using the relation :

Mean ± Zcritical * s/sqrt(n)

Zcritical at 95% = 1.96

National league :

Mean = 9.58125

Standard deviation = 1.5

9.58125 - 1.96 * 1.5/4 = 8.84625

9.58125 + 1.96 * 1.5/4 = 10.31625

(8.84625 ; 10.31625)

American League :

Mean = 9.807

Standard deviation = 0.805

9.807 - 1.96 * 0.805/sqrt(14)= 9.3853152

9.807 + 1.96 * 0.805/sqrt(14) = 10.228684

(8.84625 ; 10.31625)

A bookstore had 60 copies of a magazine. Yesterday, it sold 1/4 of them. Today, it sold 2/3 of what remained. How many copies does the bookstore have left?

Answers

The bookstore has 4 copies left

Answer:

15

Step-by-step explanation:

60×1÷4=15(1/4)

60-15=45

45×2÷3=30(2/3)

45-30=15

The point (0,0) on a coordinate grid is called

Answers

Answer:

origin

hope this helps!

Step-by-step explanation:

Answer:

Origin

Step-by-step explanation:

The origin of the graph (0,0) is the point where the two y and x axes intercept.

The origin determines every other point of the graph.  

Hope this helps!

Please help me out on this questionnnnn

Answers

Answer:

20 cubic feet.

From feet: length (ft) × width (ft) × height (ft) = cubic feet.

From inches: length (in) × width (in) × height (in) ÷ 1728 = cubic feet.

From yards: length (yd) × width (yd) × height (yd) × 27 = cubic feet.

If you need to convert to cubic feet from inches: divide the final number (i.e. the total you get after multiplying the three dimensions together

The graph of quadratic parent function f was transformed to create the graph of g(x) = f(x + 2) - 5. Which graph best represents g?​

Answers

Answer:

Step-by-step explanation:

C

f(x)= 3x+10 and g(x)= 3x-7

Answers

Answer:

1.     x=-10/3

2.    x=7/3

Step-by-step explanation:

plsssssssss mark me brainliest I need one more

Round 117.22666 to the nearest tenths

Answers

Answer:

117.2

Step-by-step explanation:

Rounding a number to the nearest tenth:

A number rounded to the nearest tenth will have one decimal place.

To do this, we look at the second decimal digit.

If it is less than 5, the first decimal digit is kept.

Otherwise, one is added to the first decimal digit.

In this question:

117.22666

The second decimal digit is 2, which means that we keep the first decimal digit which is also 2.

So, the number rounded to the nearest tenth is 117.2.

Select the true statement about triangle ABC.
A. sin A = sin C
B. sin A = cos B
C. sin A = cos C
D. sin A = tan c

Answers

B. Because that the answer I think it is
I believe the answer is B

A triangular pyramid has a base area of 74 square inches and a height of 9 inches. Which is closest to the volume of the pyramid?
a 351 cubic inches
b 702 cubic inches
c 224 cubic inches
d 234 cubic inches

Answers

Answer:

702

Step-by-step explanation:

because 74 x 9 = 666 and 702 is close

Combine like terms
x + 10x-30= -8

Answers

Answer: x=2

Isolate the variable by dividing each side by the factors that don't contain variables.

PLEASE HELP ME I NEED THE ANSWER FAST.

Answers

Answer:

126

Step-by-step explanation:

9 by 10 is 90

9 by 4 is 36

90+36= 126

Hope this helps <3

Please help me math inequality grade 8

Answers

Answer: x > 2/3

Step-by-step explanation:

-1 - x/2 < x

Simplify:

-1/2x + 1 < x

Subtract x from both sides:

-1/2x + 1 - x < x - x

-3/2x + 1 < 0

Subtract 1 from both sides:

-3/2x + 1 - 1 < 0 - 1

-3/2x < -1

Multiply both sides by 2/(-3):

2/(-3) (-3/2) < 2/(-3) (-1)

x > 2/3

Use the net to determine the total surface area. 10 cm 8 cm 8 cm 10 cm 8 cm 20 cm
440 cm2
880 cm2
144 cm2
72 cm2​

Answers

The answer to your questions is 440 cm2

Factorise
1) 9a^2 - 6a​

Answers

Answer:

9a^2 - 6a

taking common

3a(3a-2)

can someone please help me. my grade is very low in this class although i have no idea how to do this PLEASE HELP!!

Answers

Answer:

download symbolab or download photo math it gets I covered on most of that your grade should go up

Answer: How to solve equations

Step-by-step explanation:

You have to use Pemdas the order of operations to solve these types of equations.

Parenthesis,Exponents,multiplication,Division,Addition,subtraction.

Multiplication and division fit in a group left to right.

Addition and subtraction come last but depends on which comes first left to right.

Here you first have to use the distributive property.

3(y+5)=39 multiply 3 times y that gives you 3y. Then multiply 3 times 5 that gives you 15 . So, now you have simplified the left side of the equal sign so you have 3y+15=39 now subtract 15 from both sides and you get 3y=24 then you divide both sides by 3 to get y=8. What I just went over you do again and again to solve all these types of equations. Your trying to solve for the variable so you try to get y or m or n or any variable by itself.

Sam plans to use two flags on his float for the parade. Each flag is a right triangle and the triangles are similar.What is the width, x, of the larger flag in feet? halp please!!! 100 POINTS

Answers

Answer:

6.25 ft

Step-by-step explanation:

The smaller flag width is 5. And the larger flag is not that big in size. So the close answer is 6.25

Answer:

6.25ft

Step-by-step explanation:

6. Cynthia walks 6 miles at a rate of 2 miles
per hour. How long will it take her to
arrive at her destination?

Answers

3 hours is the correct answer

Answer:

3

Step-by-step explanation:

6 / 2 = 3 hours

In 2008, there were 1570 bears in a wildlife refuge. In 2010, the population had
increased to approximately 1884 bears. If this trend continues and the bear population is
increasing exponentially, find the number of bears in 2015?

Answers

Answer:

it would be about 4500 bears

Step-by-step explanation:

Please answer this also I need help

Answers

Answer: 2/2

Step-by-step explanation:

6 x 2/2 =6

Find the coordinates of the center and the measure of the radius for a circle whose equation is (x - 3)^2 + (y - 7)^2 = 2.
A. center = (3,7), radius = √2
B. center = (3,7), radius = 1
C. center = (-3, -7), radius =4
D. center = (-3, -7), radius =1

Answers

Answer:

A

Step-by-step explanation:

Equation for a circle of radius r, centered at (h,k):

(x-h)² + (y-k)² = r²

The coordinates of the center and the measure of the radius for a circle given are center = (3,7), radius = √2.

What is a circle?

A circle is a shape or a curve in a plane that has a fixed distance, called the radius, from a given point, called the center. A circle is also the set of all points that are equidistant from the center.

Given is an equation of a circle, we need to find coordinates of the center and the measure of the radius for a circle,

The equation of the circle =

(x - 3)² + (y - 7)² = 2

The standard equation for a circle of radius r, centered at (h,k):

(x-h)² + (y-k)² = r²

Comparing both we get,

(h, k) = (3, 7)

r² = 2

r = √2

Hence, the coordinates of the center and the measure of the radius for a circle given are center = (3,7), radius = √2.

Learn more about circle, click;

https://brainly.com/question/29142813

#SPJ2

Other Questions
1. Use the triangle below to determine the values indicated: The value of a movie poster is increasing at a rate of 3.5% peryear. In 1990, the poster was worth $20.25. Find the value of theposter in 2013. Question 1If a coin is flipped 3 times, what is the probability that it will show all heads?Create a tree diagram to help you answer this question.O 1/8O 3/8O 1/21/4 11. What was Archimedes claim to fame?www What is an example of rhyme scheme in the road not taken by Robert frost Solve for 3x^2-10x+8=0(SHOW YOUR WORK)QUICKLY hii they asked this again but in cm Heather drew the scaled drawing of a train car shown below. She used the scale of 2 cm = 5 ft to complete thedrawing.Train Car10.8 cmWhat is the actual length of the train car?A.21.6 ftB.27 ftC.43.2 ftD54 ft toy store is having a sale on puzzles. For each puzzle Naomi buysshe gets 75% off a second puzzle. The original price of a puzzle is $16.60.How much would 4 puzzles cost? * please help me with this question What is the simplest form of the radical expression?2+5/2-5 Bonjour Vous pouvez m aider sur les contre et le pour pour le tatouage et le piercing si ton ami veux se faire tatouer ou piercing Which statement best describes the effect of parallelism in a speech? It helps the audience remember a key word or phrase. It draws attention to a point by repeating a fact over and over. It helps engage the audience by adding rhythm and balance. It encourages the listener to think about the point the speaker is making. Help Please !!A baby bird can eat 14 feet of earthworm every day. At this rate, how many days would it take six baby birds to eat 840 feet of worms? I need help with this question I'm in 9th grade Evaluate the following expression when x = 3 and y = 5: x^2 + y^3 2+x How did the cultivation described in the source mostinfluence the building of economic interactions between the Han Dynasty and the Roman Empire?A.Silk was used as a form of currency for Roman soldiersB.Chinese merchants demanded protection from European tradersC.Silk became an important trade good in Chinese commerce with RomeD.Chinese merchants sold silkworms to European nobles wanting to produce silk Many of the protesters during the 1960s believed it was the government's responsibility to make a better life for its citizens. How can this thinking be erroneous? Suppose that an individual has a body fat percentage of 18.9% and weighs 141 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.Please respond within the hourThanks Is this a thesis statement? A nationwide ban on plastic bags is the best way to protect marine wildlife from litter.