The radius of convergence of the power series is 2, which means that the series converges for all values of x such that |x| < 2.
The function f[x] = 1/(2-x) can be expressed as a geometric series in terms of x. To do this, we use the formula for the sum of an infinite geometric series:
S = a / (1 - r),
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, we have f[x] = 1/2 * 1/(1-x/2), which has a first term of 1/2 and a common ratio of x/2. Plugging these values into the formula, we get:
f[x] = 1/2 + (x/2) * 1/2 + (x/2)^2 * 1/2 + (x/2)^3 * 1/2 + ...
Simplifying, we obtain the power series expansion:
f[x] = Σ (1/2^n) * x^(n-1), where n ranges from 1 to infinity.
Thus, we have expressed f[x] as an infinite sum of powers of x, with each term being a multiple of a power of 1/2. This power series expansion can be used to approximate f[x] for any value of x, as long as the series converges. The radius of convergence of the power series is 2, which means that the series converges for all values of x such that |x| < 2.
Learn more about power series here:
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The midpoint of AB is M(-3,-3). If the coordinates of A are (-5, -1), what are
the coordinates of B?
Answer:
The coordinates of B are (-1, -5).
Step-by-step explanation:
Since the x-coodinate of M is 2 greater than that of B (note that -3 = -5 + 2), the x-coordinate of B is found by adding 2 to -3, obtaining -1. The y-coordinate of M is -3, which is 2 less than the y-coordinate of A; Thus, the y-coordinate of B is 2 less than -3, that is, -5.
The coordinates of B are (-1, -5).
A translation is shown on the grid below
Answer:
translation of ABC to A'B'C' is 5,3
A ball falls from the top of a building. When it strikes the ground its velocity is 10 m/s. It took 5 seconds to fall. What is its acceleration? _____ m/s2
Answer:
a = 2 m/s²
Step-by-step explanation:
[tex]a = \frac{v-u}{t}[/tex]
where v is the final velocity, u is the initial velocity, and t is the time it takes. the intial velocity is always 0 m/s. given the equation, we subsitute:
[tex]a = \frac{10m/s - 0 m/s}{5s}[/tex]
a = 10m/s ÷ 5s
a = 2 m/s²
Shahida is 21 years old and Nasreen is 15 years old to Shahida after how many years will Shahida be twice as old as nasreen
Answer:
27 years
Step-by-step explanation:
21 × 2 = 42
42 - 15 = 27
Use the Distributive Property to rewrite the algebraic expression. 9(3p + 6)
wrong answers reported
Answer:
27p+54
Step-by-step explanation:
Multiply 9 to all the numbers inside the parenthesis!
Hope this helps! :)
GIVING 10 POINTS
PLEASE HELP!
What does it mean when two expressions are equivalent?
Answer:
When two equations are equivalent it means that the two equations are equal to each other. Hope this helps, thank you !!
There are 21 animals living in the barn. Some are chickens and some are horses. There are 46 legs in all. How many chickens and how many horses are in the barn?
Answer:
7 horses,and 6 chickens
6w= 12+6w divided by 2
Answer:
12w=12 divided by 2
12w=6
=2
Step-by-step explanation:
Brandy has 8 pounds of candy. She wants to give each of her friends 1/3 pound. To how many friends can Brandy give candy?
help...........................
Answer:
Could you please repeat the question?
Answer:
Answer:
Step-by-step explanation:
What help!
Thanks for free points!
Have a nice day!
only 10-11 please, giving brainliest!
que es la radicasion
Answer:
La radicación es la operación inversa a la potenciación. Y consiste en que dados dos números, llamados radicando e índice, hallar un tercero, llamado raíz, tal que, elevado al índice, sea igual al radicando. En la raíz cuadrada el índice es 2, aunque en este caso se omite.
wouldnt x+x be 2x thanks
Answer:
Wym?
---‐---------------–---------—,-------
I'll answer it on the comment or are u just playing?
the questipn is: Given segment AB with endpoint (-2,-2) and (8,4), what is the coordinate of the midpoint?
Answer:
(3,1)
Step-by-step explanation:
If you plot both of the points on a graph you get another straight line.
When you connect the dots you get 3,1 as the midpoint of the two segments :))
Will give brainliest!
Answer:
Step-by-step explanation:
Equation for line a:
x = - 4
Equation for line b:
x = 4
Equation for line c:
y = 4
Equation for line d:
y = - 2
Equation for line e:
y = − 0.75x + 1
14 Customers into the store over the course of seven minutes how many Internet store after one minute
Answer:
2
Step-by-step explanation:
14 divided by 7 is two customers in one minute
Answer:
After one minute there will be 2 people inside the store.
Step-by-step explanation:
First we put this into a proportion. Aka set up like a fraction.
14 (customers) x
------- ---> ------
7 (minute) 1 minute
In order to find x, we must divide by 7 because in order to make the bottom number one on the bottom, you must divide by 7 , so we do the same to the top.
14/7 is 2.
This means that per minute, there are 2 people inside the store.
After one minute, There will be 2 people inside the store.
2hours 24mins in fraction
Answer:
2 2/5
Step-by-step explanation:
2 24/60 = 2 2/5
there are 60 minutes in an hour so you can just put 24 over 60 and the two outside to write it as a mixed number fraction then reduce. If you want to write it as a improper fraction you can multiple 2 times 5= 10 then add 2 to get 12/5
Which pair of fractions is not equivalent fractions?
A.1/9,2/18
B.7/8,5/6
C.3/16,9/48
D.6/15,4/10
A dress with a regular price of $60 is on sale for 20% off the regular price. Lisa has a coupon for an additional 10% off the sale price. What is the price of the dress after the discount for the coupon?
Answer:
It is $42
if I am wrong then let me know so I can recheck my work
Answer:
$42
Step-by-step explanation:
20+10=30%
60*0.3=18
60-18=42
Fay has a lemonade stand.
She spends £42 on ingredients.
She sells each glass of lemonade for £1.20.
If she sells 50 glasses of lemonade, what is her total profit?
Answer:
she made a profit of 18$
50*1.2=60-42=18
Step-by-step explanation:
m> 32
Which of the following could be a possible value for m?
32
33
100
n 31
Please help me! 20 points!
Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the solution of the equation?
(its in the attachment)
Thank u lovely
Step-by-step explanation:
This is a edit. The answer is 30. Brainly won't save my work.
[tex]3 \sqrt[5]{ {(x + 2)}^{3} } + 3 =27 \\3 \sqrt[5]{ {(x + 2)}^{3} } =24 \\ \sqrt[5]{ {(x + 2)}^{3} } = 8 \\ {(x + 2)}^{3} = {8}^{5} \\( x + 2) = \sqrt[3]{ {8}^{5} } \\ ( x + 2) = 32 \\ x = 30[/tex]
12-b=12.5. Solve each equation
‘Basic exponent rules’ simplifying to a single power .
Answer:
64
Step-by-step explanation:
please help!!
List the temperatures shown on the table in order
from least to greatest:
Temperature (°F)
Thursday
-8
Friday
7
Saturday
18
Sunday
-11
sunday: -11
thursday: -8
friday: 7
saturday: 18
Which of the following best describes the equation below?
y = -3x - 13
A.
both linear and nonlinear
B.
nonlinear
C.
neither linear nor nonlinear
D.
linear
Answer:
d. linear
Step-by-step explanation:
using the format y=mx+b
Help please
|2x + 5| = 11
Step-by-step explanation:
[tex]2x + 5 = 11 \\ 2x = 11 - 5 \\ 2x = 6 \\ x = 6 \div 2 \\ x = 3[/tex]
can someone solve this
Select the correct answer.
A ball is thrown up from a height of 400 feet, and the height (in feet) of the ball at any time t, in seconds, is given by the function shown below.
[tex]h(t)=-16t^{2}+400[/tex]
Find the equation for the axis of symmetry of the given function.
A.
t = 0
B.
t = 5
C.
t = 6
D.
t = 4
Answer:
A
Step-by-step explanation:
Because i took the the test
Does anyone know how to solve this?
Answer:
A point in polar coordinates is written as (R, θ)
If we want to transform this point to rectangular coordinates, we get:
x = R*cos(θ)
y = R*sin(θ)
Now we can remember that the sine and cosine functions have a period of 2*pi, then:
cos(θ) = cos(θ + 2*pi)
or:
cos(θ) = cos(θ + 2*pi + 2*pi)
and so on.
Then the point (R, θ) is the same as (R, θ + 2*pi) and (R, θ + k*(2*pi))
where k can be any integer number.
Then if we have a point in polar coordinates:
(-4, -5*π/3)
Then another two polar representations of this point are:
(-4, -5*π/3 + 2*π) = (-4, -5*π/3 + 6*π/3) = (-4, π/3)
Now we can not add 2*π (nor subtract) because we would have an angle outside the range [-2*π, 2*π]
For example, if we have:
(-4, π/3 + 2*π) = (-4, 7*π/3)
And we can not change the value of the radius and get the coordinates for the same point.
So another representation could be something like:
(-8/2, π/3)
Where i just wrote -4 in another way.
Now, a really important point.
When working with polar coordinates, we always use R as a positive number (here you can see that R is negative) so this is not the standard notation for the polar representation of a point.