Let g (t) = 1/1+4t2, and let be the Taylor series of g about 0. Then: a2n = for n = 0, 1, 2, . . . A2n+1 = for n = 0, 1, 2, . . . The radius of convergence for the series is R = Hint: g is the sum of a geometric series.

Answers

Answer 1

The Taylor series of g about 0 is given by 1 - 4t^2 + 16t^4 - 64t^6 + ... The coefficients a2n and a2n+1 are given by a2n = (-1)^n * 4^n/(2n+1) and a2n+1 = 0. The radius of convergence for the series is R = 1/2sqrt(2).

The Taylor series of g about 0 is given by:

g(t) = ∑[n=0 to infinity] ((-1)^n * 4^n * t^(2n))/(2n+1)

That this is the sum of a geometric series with first term a=1 and common ratio r=-4t^2. Therefore, we can use the formula for the sum of an infinite geometric series to get the Taylor series of g. The formula is:

S = a/(1-r)

Plugging in our values, we get:

g(t) = 1/(1+4t^2) = 1 - 4t^2 + 16t^4 - 64t^6 + ...

To find the coefficients a2n and a2n+1, we just need to look at the terms that have even and odd powers of t:

a2n = (-1)^n * 4^n/(2n+1)

a2n+1 = 0

The radius of convergence for the series is R = 1/2sqrt(2). We can see this by using the ratio test:

lim[n→∞] |a_n+1/a_n| = 4t^2/(2n+3) → 1 as n → ∞

Therefore, the series converges for |t| < 1/2sqrt(2).

To know more about geometric series, visit;

https://brainly.com/question/24643676

#SPJ11


Related Questions

helpppp meeee plz...

Answers

Answer:

3 coefficient po

Step-by-step explanation:

sana maka tulong

Perimeter? =
Area? =

Answers

Answer:

Your answer is

Area  = 16.23

perimeter = 24

Mark my answer as brainlist . I need that urgently . Folow me for more answer.

Step-by-step explanation:

Solve for x. Round to the nearest tenth as needed

Answers

Step-by-step explanation:

by Pythagoras :

H²= B²+ P²

(7+x)²= x²+ 9²

49 + 14x + x² = x²+81

14x = x² -x²+81 - 49

14x = 32

x = 32/14 = 16/7 = 2.28 cm = 2.30 cm

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you .

Determine whether the second polynomial is a factor of the first.
6x2 + 5x +54; x-4
Select the correct choice below and fill in the answer box to complete your choice.
O A. No, because the polynomial 6x² + 5x + 54 evaluated at 4 is equal to
OB. Yes, because the polynomial 6x + 5x +54 evaluated at - 4 is equal to
OC. No, because the polynomial 6x + 5x +54 evaluated at - 4 is equal to
OD. Yes, because the polynomial 6x + 5x + 54 evaluated at 4 is equal to

Answers

Answer:

No, because the polynomial 6x² + 5x + 54 evaluated at 4 is equal to 170.

Step-by-step explanation:

A polynomial should have a factor (let's say a) that would make the polynomial equal to zero when we substitute that factor (a) into the polynomial.

A cat leaps from the ground into the air with an initial vertical velocity of 11 ft/s. After how many seconds does the cat land on the ground?

Answers

Answer:

11/16 of a second

Step-by-step explanation:

3x-2.(x+1)=-2 denklemini sağlayan, x'in değeri kaçtır? ​

Answers

Answer:

3x - 2(x +1) =-2

3x - 2x - 2 =-2

x = - 2 +2

x = 0

hope it helps

At the market you can buy six bags of apples for $25 at the archer you can get eight bags of Apple for $35 which is the better deal

Answers

Answer:

$25

Step-by-step explanation:

$ 25 the correct answer

help pls ;;-;; ye thxs

Answers

Answer:

You still need help? :P

Step-by-step explanation:

Can anyone please help me this these questions:

1. $.50 is what percent of $2.00
2. $.02 is what percent of $2.00
3. $2.00 is what percent of two dollars

Answers

Answer:

1.

[tex]25\%[/tex]

2.

[tex].04\%[/tex]

3.

[tex]100\%[/tex]

Answer:

1 is 25% because .50 going into 2 00 4 times or 35%

2 is 10% because 02. is 10% of 2.00

4 is 100% because its all of the 2.00

A salesperson at a jewelry store earns ​8% commission each week. Last​ week, Ali sold $450 worth of jewelry. How much did Ali make in​ commission? How much did the jewelry store make from her ​sales?

Answers

Answer:

she earned 36$ and the store earned 409.5

Step-by-step explana

8% of 450

91% of 450

Christina wants to buy shirts that cost $17.00 each. If x represents the number of shirts Christina buys, which equation shows the amount of money (M) she will pay for the shirts?

Answers

Answer: 17x

Step-by-step explanation:

From the question, we are informed that Christina wants to buy shirts that cost $17.00 each and we are further told that x represents the number of shirts Christina buys.

The equation shows the amount of money (M) she will pay for the shirts will be gotten by multiplying the amount of the each shirt by the total number of shirts bought. This will be:

= 17 × x

M = 17x

y/-9=1/18 solve for y

Answers

Answer:

y=-1/2

Step-by-step explanation:

Why do economists use market values when calculating GDP?

Answers

Answer:

Economists use market values when calculating GDP, because if they used quantity terms, they would have multiple units of measurement. Whereas, when they use market values, they have one unit of measurement for all products and services.

Step-by-step explanation:

Dn80 pipe 88millimeters is According to the plan All openings must be 40mm larger than the pipe. You know that

Answers

Answer:

128mm

Step-by-step explanation:

Given

[tex]Pipe = 88mm[/tex]

[tex]Ope\ nnings = 40mm\ larger[/tex]

Required

Determine the length of the openings of the pipe

To do this, we simply add 40mm to the length of the pipe.

This gives:

[tex]Ope\ nings = 88mm + 40mm[/tex]

[tex]Ope\ nings = 128mm[/tex]

Hence, the opening must be 128mm

cupcakes and points for those who answer this question for me
(the screenshot)

Answers

Answer:

2.06

Step-by-step explanation:

The original decimal is 2.0625.

Since the thousandths place is 2, we can't round up. So we can keep the 6 which is in the hundredths place giving us 2.06

HELP I NEED HELP ASAP

Answers

Answer:

C) Linear

Step-by-step explanation:

To find this, I turned the situation into an expression. The expression representing this would be: 2x + 5 (a linear function). The 2x represents how much his dad gives Joseph weekly. The 5 represents how much Joseph already has.

Hope it helps!

0.75 divided by 38.652

Answers

Answer:

0.019404

Step-by-step explanation:

0.75/38.652 is 0.019404.

Answer:

Divide  0.75  by  38.652  =

0.01940391

and

Divide  38.652  by  0.75 =

51.536

Step-by-step explanation:

Chad has a rope that is 24 yards long. How many pieces of rope measuring 4/7 of a yard can he divide his rope into?

Answers

Answer:

42

Step-by-step explanation:

Chad has a rope that is 24 meters long

He wants to divide the rope so each piece will be 4/7 yards

= 24÷ 4/7

= 24× 7/4

= 168/4

= 42

Hence he can divide the rope into 42 pieces

What is the slope of the line that passes through the points (3, -20) and (11, 16)?
please I'm being timed

Answers

Answer:

9/2

Step-by-step explanation:

(3, -20) & (11, 16)

To find the slope of the line that passes through these points, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(16 - (-20)) / (11 - 3)

Simplify the parentheses.

= (36) / (8)

Simplify the fraction.

36/8

= 9/2

9/2 is the most simplified fraction. This is your slope.

Hope this helps!

What is the value of x?​

Answers

x= 67°

hope that helps:)

workout the value of 2^0

Answers

Answer:

It just equals to 2

Step-by-step explanation:

Think of it as 2^1!

1.

The value of anything that has an exponent of 0 is always 1

A jewelry box has a volume of 14 cubic inches. The area is 7 square inches. What is the height of the jewelry box.

Answers

Answer:

2 inches

Step-by-step explanation:

a=Lw

v=lwh

lw= 7

14/7=2

7:5 is equivalent to...?​

Answers

Answer:

6:0

Step-by-step explanation:

Thank me later :)))))))))

The square of an add number is

Answers

The power of is what it’s called

Evaluate the expression when a=5 and b= -5.
-a +8b

Answers

We would just have to plug the numbers where the variables are.
- (5) + 8(-5)
-5 + -40
- 45 is your answer
-a + 8 b
-(5) + 8(-5)
-5 - 40
= -45

The bill at the restaurant was $18.79 estimate the amount to leave as a $10 tip

A. $2.00
B. $3.00
C. $9.00
D. $21.00

Answers

It has to at least be 9.00 bc i got 8.79

Linda is making a mosaic stepping stone to place in
her garden. The stone is shown below. How much
mosaic glass tile will Linda need to cover the surface
of five stepping stones? Use 3.14 for pie.

Help please lol

Answers

Answer:

D 565.2 in

Step-by-step explanation:

First you need to find the area of the stepping stone. The rule for area of circle is pi times radius squared. To find the radius you divide 12 by 2 = 6. After you do 6 times 6= 36 you multiply 36 times pi (3.14) = 113.04. After we find the are of the stepping stone we multiply it by five to get how many inches we have to cover. 113.04 times 5= 565.2 in.

Solve the system of equations 2x - 2y = - 14 and 2x + 6y = - 6 by combining the equations.

Answers

sorrryy I don't know how to delete this so...

Step-by-step explanation:

step 1. first combine by subtraction.

step 2. 0x -8x = -8

step 3. y = 1

step 4. x = -6.

step 5. the answer is (-6, 1).

An air conditioning repair company has a flat
service fee and charges an hourly rate. One
customer pays $180 for two hours of work.
Another pays $230 for three hours of work.
Write a linear function for this situation. Use h
For the number of hours.
C(h) =

Answers

Answer:

Step-by-step explanation:

Is it possible to construct a triangle with sides of lengths 40, 8, and 30?

Answers

Answer:

No, the two shorter sides must exceed the longer side.

Step-by-step explanation:

Other Questions
The equation below represents the process that you observed. Balance the equation. What type of reaction?6CO2 + 6H2O + light energy = 0C6H12O6 + 6O2 _______________________ what is these in simplest form a) 2a + 4 + 5a + 8 = b) -2b 7 + 3b 8 = how is christmas mardi gras easter and rome connected? If there was a point R(-2, 4) and it was dilated to R'(-8, 16), what was the scale factor? * HELP ASAP!!!!!!!!Find the cite of each variabile The temperature outside changed from 64F to 43F over a period of seven days. If the temperature changed by the same amount each day, what was the daily temperature change? A seabird is 28 meters above the surface of the ocean. What is its elevation? Learning Task 2: Fill in the blanks. Write your answers on a separateBreeding groundmarineAquaticroots of the seacoastalIf there are no mangrove forests, then the sea will have no meaning.It is having a tree with no roots, for the mangroves are theMangrove swampswamp are found along the 2. area They areimportant to 3.life. They are serve as 4.ground for fishesand marine organism. They protect the 5.__from erosion and effects ofstorms.science po yan What is the measure of arc FG?PLEASE HELP , ill make BRAINLIEST Amelia bought 40 plain black T-shirts for $4 each.She painted designs on them and then sold each T-shirt for 7.50.How much profit did Amelia make selling her fancy T-shirts? Which map shows how Philip II unified the Greek city-states?A section of Greece is shaded.Crete, the islands in the Aegean Sea, and several countries in Europe are shaded.Crete, the islands in the Aegean Sea, several countries in Europe, and Asia Minor are shaded. Please please help with this question , you will get 10 points if you answer this question, dont get bothered with 1 point written in question. 1. 12x 8x + 4 = 20 2. 9w + 4w 5w + w = -9 Arid, physical region found in North AfricaA. Atacama Desert B. Gobi DesertC. Sahara Desert D. Steppe 1. Which of the following refers to the process of an environment constantly changing?"energy cycleenergy successionecological cycleecological succession State any five causes of the empty treasury of France under Louis XVI. Gizmos Warm Up Energy constantly changes from one form to another, but in a closed system, the total amount of energy always remains the same. This concept is known formally as the law of conservation of energy The Energy Conversion in a System Gizmo allows you to observe the law of conservation of energy in action. In the Gizmo, a suspended cylinder has gravitational potential energy. When the cylinder is released, the gravitational potential energy is converted into kinetic energy, which causes the stirrer in the water to spin. 1. What is the initial temperature (T) of the water? Question: 1 out of 10~!! Volume !!~ Write a story for an English speaking magazine that begins with these words: They all felt as if they were standing on top of the world. ( 140-190 words) What is the freezing point of a solution of 498mL of water (solute) dissolved in 2.50 L of ethanol (solvent), C2H5OH? The density of C2H5OH is 0.789g/cm3. (Remember that water has a density of 1.0 g/cm3.)