The power series representation for f(x) = arccot(x) is
[tex]\pi /2- \lim_{n \to \infty} (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]
The power series ∑aₙxⁿ is an infinite series and looks like a function of x. An easy way to illustrate the idea of a power series representing a function is to use the geometric series as an example.
The power series is a very important kind of infinite series where the terms contain the powers of a variable. A power series is a series of the general form:
∑aₙ(x-x₀)ⁿ=a₀+a₁(x-x₀)+a₂(x-x₀)²+a₃(x-x₀)³+.........
called a power series centered at x₀
where x is a variable,
x₀ is a real constant, and the
aₙ's are real constants called the coefficients of the series.
The given power series representation is f(x) = arccot(x).
we observe that f '(x)=-1/(1+x²) and find the required series by integrating the power series for -1(1+x²)
arccot(x)=∫-1/(1+x²)dx
⇒∫-(1-x²+x⁴-x⁶+....)dx
⇒C-x+1/3x³-x⁵/5+1/7x⁷-......
To find C we put x=0 and obtain C=arccot(0)=π/2
Therefore,
C=π/2-x+1/3x³-x⁵/5+1/7x⁷-.......
f(x)=π/2- ∑(-1)ⁿₓ x^2n+1/2n+1
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Carly purchased pints of ice cream for a party. If each guest will be served exactly
pint of ice cream, what is the greatest number of guests that Carly can serve?
Answer:
I do not understand the question I am so sorry :(
Step-by-step explanation:
what is the probability that the red shows a six or the green die shows a six?
Answer:
11/36
Step-by-step explanation:
The amount of time needed to complete a certain roadtrip, t, varies inversely with the speed of a vehicle, s. At a speed of 52 miles per hour, the trip will be complete in 12 hours. How many hours would it take at a speed of 48 miles per hour?
Do not include the units in your answer.
At a speed of 48 miles per hour, it would take 13 hours.
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given:
The amount of time needed to complete a certain road trip, t, varies inversely with the speed of a vehicle, s. At a speed of 52 miles per hour, the trip will be complete in 12 hours.
Distance is constant.
And we know the formula:
Distance = speed x time
= 52 x 12
= 624 miles
Now to find the time:
Now for speed = 48 miles per hour
time,
t = distance / speed
= 624/48
= 13 hours
Therefore, 13 hours would it take at a speed of 48 miles per hour.
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Exit
Justin is going to the school dance. He went to the mall and bought two new shirts for $21.99 each and a new pair of dress shoes for $45.59. Which two operations would be used in order to figure out how much he spent at the store?
A. multiply and add
B. add and subtract
C. multiply and subtract
D. divide and add
Answer:
its letter A multiply and add
Please help, this is due soon
Answer:
4
Step-by-step explanation:
If I remember correctly you can not have the arrows on the same y axis
PLEASE HELP I NEED THE VALUES OF M AND P!!!!!!!! WILL GIVE BRAINLIST!!!!
Answer:
m=5 and p=4
Step-by-step explanation:
The ratio of cows to goats in a farm is 3:2 if there are 210 more cows than goats how many animals are there in the farm
[tex] {a}^{2} {a}^{4} {a}^{5} answer \: a40 \: or \: a11 [/tex]
Question Help
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11.3.IP-8
John is knitting a blanket. He records the length he knits each day. How many more inches does
John need to knit so the blanket is 54 inches?
I'm not sure. Don't be angry but this is my first time on this app but it helps a lot and i would also like to help but it seems that I'm the one who needs help.
To begin a bacteria study, a petri dish had 2800 bacteria cells. Each hour since, the number of cells has increased by 7.2%. Let t be the number of hours since the start of the study. Let y be the number of bacteria cells. Write an exponential function showing the relationship between y and t.
2 1/3 x (-3 2/7) what does it equal I’m doing “multiplying signed fractions”
what is the solution for 5(m-3) ≥ 7m-2.4 ?
Answer:
Step-by-step explanation:
5(m-3)≥7m-2.4
5m-15≥7m-2.4
2m≤-12.6
m≤-6.1
Answer:
m>6.3
Step-by-step explanation:
The radius of a quarter circle is 2 yards. What is the quarter circle's perimeter?
If you can answer these simple questions im giving brainly :)
Answer:
65 3 46
Step-by-step explanation:
Answer:
a² + 1 = 65
18/2a = 3
6(d + 8) - 10d = 46
Step-by-step explanation:
a² + 1 when a = 8
first, plug in 8 for a.
a² + 1 ⇒ 8² + 1begin simplifying by finding 8², which is just 8 · 8.
8² + 1 ⇒ 64 + 1finish simplifying by adding 64 + 1.
64 + 1 = 65therefore, when a = 8, a² + 1 = 65.
18/2a when a = 3
first, plug in 3 for a.
18/2a ⇒ 18/2(3)begin simplifying by multiplying 2 · 3.
18/2(3) ⇒ 18/6finish simplifying by dividing 18 ÷ 6.
18/6 = 3therefore, when a = 3, 18/2a = 3.
6(d + 8) - 10d when d = 1/2
(i'm going to convert 1/2 to 0.5 because i prefer working with decimals rather than fractions)
so... 6(d + 8) - 10d when d = 0.5
first, plug in 0.5 for d.
6(d + 8) - 10d ⇒ 6(0.5 + 8) - 10(0.5)begin simplifying by distributing 6 to 0.5 and 8, which is just 6 · 0.5 and 6 · 8.
6(0.5) = 36(8) = 48after distributing, your expression is 3 + 48 - 10(0.5).
continue simplifying by multiplying -10 · 0.5.
3 + 48 - 10(0.5) ⇒ 3 + 48 - 5add 3 + 48.
3 + 48 - 5 ⇒ 51 - 5finally, finish simplifying by subtracting 5 from 51.
51 - 5 = 46therefore when d = 1/2 or 0.5, 6(d + 8) - 10d = 46.
i hope this helps! have an amazing day <3
On a map, Breanne measured the distance (as the crow flies) between Los Angeles, California and San
Francisco, California at 2 inches. The scale on the map is 1/4 inch = 43 miles. What is the actual
straight-line distance between Los Angeles and San Francisco?
Jake is a factory manager for a company that produces batteries. Occasionally, some are found to be defective. Based on previous results, Jake
estimates that 12 batteries will be defective for a certain month. However, 10 were actually defective. What is the percent error of Jake's estimate?
The percent error of Jake's estimate is 16.6 % when he found 10 were actually defective out of 12 batteries.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Mili obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.
Jake calculates that 12 batteries will be faulty during the month given in the question.
To determine the percent error which is the percentage of the difference between the accepted value and the experimental value.
As per the given condition, the required solution would be as:
⇒ [(12 - 10)/12] × 100
= [(2/12)] × 100
= [1/6] × 100
= 0.166× 100
= 16.6 %
Thus, the percent error of Jake's estimate is 16.6 %.
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Please help me in struggling with this
Answer:
Step-by-step explanation:
21
16
27
15
70
Answer:
Step-by-step explanation:
Hello!
I think I can help.
Lets use the first problem and walk through it and I think it could help you with the others.
3/7 = ?/49
So basically with these problems you are working backwards. You are working right to left and dividing to figure out what you will need to multiply the other part of the fraction by.
So here we have 49 and 7 that line up with each other. (Always look for the fractions that line up horizontally)
Going right to left and dividing :
49 / 7
= 7
So we know that it was 7 x 7 to get that 49
So now we used the number we just found by dividing (7) and multiply it left to right by the other number to find the missing number (?).
If we do this we do :
3 x 7
= 21
And that is the missing number !
We plug that in right where the blank is (?) and we get :
3/7 = 21/49
I am not sure if you have to simplify this but you cant anyways. If you have questions about simplifying ask in the comments.
To check this we can actually multiply the side that had two numbers to begin with (the left side numbers) and multiply it by the number we found by dividing (7).
So we do this with 3/7 :
3 x 7 = 21
7 x 7 = 49
if we plug this back in we get :
21/49 = 29/49 and we know this is correct.
I hope this helps you solve the other problems. If you have any questions or are still confused with others please message me or comment and I will do what I can to help. :)
5. David Read's the problem:
Ally bought a T-shirt and a pair of shorts on sale which
reduced prices by 1/4. The total savings on the 2
garments was $10.25. Find the original price for the
pair of shorts.
David says that the original price of the shorts was $41.
Does his answer seem reasonable? Defend your
answer by writing and solving an equation that
represents the situation.
Answer:
No, David's answer does not seem reasonable.
Let x= original purchase amount
25x = $10.25, so solve for x by dividing both sides by .25, and you get x = $41.
If the shirt was $18, the shorts must have been $41-$18 = $23 NOT $41.
Step-by-step explanation:
Aaron mows lawns and makes $70 per week. Last week
he spent $15 on gas and spent 5 hours mowing all of the
lawns. How much did he earn per hour?
Bonnie has 4 sharpened and 8 unsharpened pencils in her pencil case. She randomly selects 2 of the pebcils from the box without replacement. What is the probability that both pencils will be sharpened? A. 1/2 B.1/9 C. 4/33 D.1/11
Answer:
D. 1/11.
Step-by-step explanation:
There are 12 pencils in the case.
Prob( first one is sharpened) = 4/12 = 1/3
Prob(second is sharpened) = 3/11
Prob(both sharpened) = 1/3 * 3/11
= 3/33
= 1/11.
The probability is 1/11 that both pencils will be sharpened which is the correct option(D).
What is probability?The probability is defined as the possibility of an event being equal to the ratio of the number of outcomes and the total number of outcomes.
Given that,
Bonnie has 4 sharpened and 8 unsharpened pencils
So, there is a total of 12 pencils in the pencil case.
Let, the probability first one is sharpened is P(E₁)
The probability second one is sharpened is P(E₂)
P(E₁) = 4/12 = 1/3
P(E₂) = 3/11
Required probability both sharpened P(E) = P(E₁)×P(E₂)
Required probability both sharpened P(E) = 1/3 × 3/11
Required probability both sharpened P(E) = 3/33
Required probability both sharpened P(E) = 1/11.
Hence, the probability is 1/11 that both pencils will be sharpened.
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A rectangle has an area of 64 ft squared. If the length of the rectangle is x ft and the width of the rectangle is x to the 1/2 ft, find the length and width of the rectangle.
Answer:
I DONT KNOW BUT YOU HAVE TO CHECK OUT MY QUESTION NO OE CAN SOLVE IT I BET
Step-by-step explanation:
A function and its inverse are shown on the graph.
y
y
6
f(x)
4
Which answer pairs a possible domain restriction
for f(x) and its corresponding impact on f'(x)?
O f(x) domain: x 2 1
f'(x) domain: x 2 1
Of(x) domain: x 2 1
f'(x) range: y21
Of(x) domain: XS-2
f'(x) domain: x = -2
Of(x) domain: xs-2
f'(x) range: ys-2
2.
x
+
-2
2
4
6
-2
f (x)
-6
Answer:
not: f(x) domain: x ≤ -2
f^-1(x) range: y ≤ -2
Step-by-step explanation:
The possible domain restriction for f(x) and its corresponding impact on f'(x) is f(x) domain: x < 1, f'(x) domain: x < 1.
How to find the function which used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
We are given that;
The graph of function
Now,
Looking at the graph, we can see that the function and its inverse are reflections of each other across the line y = x. This means that the domain of the inverse function corresponds to the range of the original function, and vice versa.
From the graph, we can see that the original function f(x) has a vertical asymptote at x = 1. This means that the function is undefined at x = 1.
Therefore, a possible domain restriction for f(x) is x < 1, which would exclude x = 1 from the domain. The corresponding impact on f'(x) would be that f'(x) would also be undefined at x = 1.
So, the answer that pairs a possible domain restriction for f(x) and its corresponding impact on f'(x) is:
f(x) domain: x < 1
f'(x) domain: x < 1
This is because the domain of f(x) is restricted to exclude x = 1, and the corresponding impact on f'(x) is that it is also undefined at x = 1.
Therefore, by the graphed function the answer will be f(x) domain: x < 1, f'(x) domain: x < 1.
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A rectangle has a length of (x+3) centimeters and a width of 1/2 x centimeters. If the perimeter is 24 centimeters, what is the length of the rectangle?
Answer:
Step-by-step explanation:
Perimeter = 2L + 2W = 24
L+W = 12
(x+3)+(x/2) = 12
2x+6 +x = 24
x = 6 cm
L = x+3 = 9 cm
s2t-10
if s = -8 and
T= 3/4 please show how you got the answer
Complete the function table,
then list the domain of the function
Domain
What’s the next numbers ?
Answer:
f(x)=x-2
f(2)=2-2=0
f(3)=3-2=1
you only have attach the number to x
Answers:
Second row: 0Third row: 3-2 and 1====================================================
Explanation:
The first column is the list of x values we plug into the function. The second column describes what happens to those x inputs. Namely, we subtract off 2. In the first row, it shows 0-2 after replacing x with 0. This leads to the result of -2 since 0-2 = -2.
In the second row, we have the input x = 2 turn x-2 into 2-2 = 0. So that's why 0 goes in the blank for the second row.
In the third row, we have x-2 = 3-2 = 1. So we'll have 3-2 go in the first blank of row 3, and the value 1 go in the second blank of this same row.
you are working to save money for a trip you need to save 1500 you already saved $250 saved, and make $10 an hour at your job whites and solve an equation to represent how many hours, h, you need to work to make the rest of the money
Answer:
125 hrs
Step-by-step explanation:
1500-250=10h
simplify
1250=10h
divide both sides by 10
h=125
125 hrs
There are 285 sixth graders going on a class trip to the museum.each bus can hold
25 students. How many buses will be needed to transport all the students? Will all the buses be fuller? If not how many students will be on the last bus.
the buses be filled? If not, how many stuc
Answer:
12 Busses
10 in the last bus
Step-by-step explanation:
275 in 11 busses and 10 in 12th bus
81.04 x 0.010 answer please
Answer:
0.8104
Step-by-step explanation:
Answer:
0.8104
Step-by-step explanation:
Take the 0 out of the end of the 0.010 because there is no reason for it to be there.
Then you just multiply 81.04 by 1 because the rest of 0.01 is just zeros and the you get 81.04.
Then you count the decimal places in 0.01 which you get two so you move the decimal in 81.04 two times to the left.
Your answer should be .8104
I hope this helps!!!!
Given the points (-5,-7) and (-2,-8), calculate
the slope.
(I NEED THIS ANSWER ASAP!)
Answer:
Slope is -1/3
Step-by-step explanation:
(-5,-7)(-2,-8)
-8+7/-2+5
-1/3
m=-1/3
Answer:
Slope=-1/3
Step-by-step explanation:
What is the value of y?
2y
Y+10
50°
Answer:
The question is incorrect. Please rewrite the question.