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).
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Evaluate the expression when a=5 and b= -5.
-a +8b
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?
Answer:
11/16 of a second
Step-by-step explanation:
Is it possible to construct a triangle with sides of lengths 40, 8, and 30?
Answer:
No, the two shorter sides must exceed the longer side.
Step-by-step explanation:
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
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.
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
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.
The square of an add number is
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
helpppp meeee plz...
Answer:
3 coefficient po
Step-by-step explanation:
sana maka tulong
cupcakes and points for those who answer this question for me
(the screenshot)
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
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
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
What is the slope of the line that passes through the points (3, -20) and (11, 16)?
please I'm being timed
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!
Solve the system of equations 2x - 2y = - 14 and 2x + 6y = - 6 by combining the equations.
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).
workout the value of 2^0
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
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
Answer:
$25
Step-by-step explanation:
A salesperson at a jewelry store earns 8% commission each week. Last week, Ali sold $450 worth of jewelry. How much did Ali make in commission? How much did the jewelry store make from her sales?
Answer:
she earned 36$ and the store earned 409.5
Step-by-step explana
8% of 450
91% of 450
A jewelry box has a volume of 14 cubic inches. The area is 7 square inches. What is the height of the jewelry box.
Answer:
2 inches
Step-by-step explanation:
a=Lw
v=lwh
lw= 7
14/7=2
0.75 divided by 38.652
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:
What is the value of x?
x= 67°
hope that helps:)
7:5 is equivalent to...?
Answer:
6:0
Step-by-step explanation:
Thank me later :)))))))))
3x-2.(x+1)=-2 denklemini sağlayan, x'in değeri kaçtır?
Answer:
3x - 2(x +1) =-2
3x - 2x - 2 =-2
x = - 2 +2
x = 0
hope it helps
Perimeter? =
Area? =
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:
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?
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
Solve for x. Round to the nearest tenth as needed
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 .
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) =
Answer:
Step-by-step explanation:
HELP I NEED HELP ASAP
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!
y/-9=1/18 solve for y
Answer:
y=-1/2
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?
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
help pls ;;-;; ye thxs
Answer:
You still need help? :P
Step-by-step explanation:
Why do economists use market values when calculating GDP?
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
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