evaluate the indefinite integral as an infinite series. cos(x) − 1 x dx [infinity] n = 1 c

Answers

Answer 1

The indefinite integral of cos(x) - 1/x dx as an infinite series can be expressed as ∑((-1)ⁿ * x²ⁿ / (2n)!) - ln(x) + C, from n = 0 to infinity.

To evaluate this integral, we first find the power series representation of cos(x) and then integrate term by term:

1. The Maclaurin series for cos(x) is: ∑((-1)ⁿ * x²ⁿ / (2n)!), from n = 0 to infinity.
2. Integrate the cos(x) term: ∫cos(x) dx = ∑((-1)ⁿ * x²ⁿ⁺¹ / ((2n+1) * (2n)!)), from n = 0 to infinity.
3. Integrate the 1/x term: ∫(-1/x) dx = -∫(1/x) dx = -ln(x).
4. Combine the results and add the integration constant: ∑((-1)ⁿ * x²ⁿ⁺¹ / ((2n+1) * (2n)!)) - ln(x) + C, from n = 0 to infinity.

To know more about indefinite integral click on below link:

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Related Questions

34-60 how much apples are they left

Answers

Answer:

60-34= 26

Step-by-step explanation:

Lin borrowed 950 for a new laptop. She will pay $25,80 each month for the next 48 months (2 years). Find the amount of
interest Lin will be paying for her loan.
interest Lin will be paying for her loan

Answers

Answer:

288,40 $

Step-by-step explanation:

25,80$ / month * 48 months = 1238,40$ total payment.

1238,40$ - 950$ (borrowed) = 288,40 $ payed in interest.

Help!!! Please HELP!!!

Answers

Answer:

Step-by-step explanation:

that's where they cross

Select the correct answer.

What are the factors of the function represented by this graph?

A. (x − 4) and (x − 8)
B. (x − 4) and (x + 8)
C. (x + 4) and (x − 8)
D. (x + 4) and (x + 8)

Answers

The factors of the function represented by the graph are (x + 4) and (x - 8)

How to determine the factors of the function represented by the graph?

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that:

The graph intersects with the x-axis at x = -4 and x = 8

So, we have

x = -4 and x = 8

Set the equations to 0

So, we have

x + 4 = 0 and x - 8 = 0

This means that the factors of the function represented by the graph are (x + 4) and (x - 8)

Answers

Step-by-step explanation:

you can use any two points on the graph but I used the easiest one. It doesn't matter it will give the same result

need help in this show working please

Answers

this is what i got hope it helps

line pass through the sets given points. which choice shows perpendicular lines?

Answers

Answer:

I have no reference to this question, there is no graph or anything to show me.

Step-by-step explanation:

The cheerleading squad at Kensington High School had 18 members with the old coach. Now, with the new coach, there are 50% more members on the squad, how many members are on the squad now

Answers

Answer:

27 members

Step-by-step explanation:

So we have 18 members and we see a 50% increase in members.

So:

Now the squad is 150% of 18

We can set up a percent proportion

x/150=18/100

To solve, we do:

(150*18)/100 = x

27 = x

There is an easier way to do this with benchmark fractions.

We find 50% of 18 which is 9

And since it's a 50% increase, we add 9 to 18 and get 27

Let me know if you have any questions

Answer:

B) 8 + J

(It's saying my answer is too short, not too sure why)

Gilligan sees a ship coming close to the shore hes standing on.

Answers

i think part a is: yes because both triangles are right angles. it would be postulate SAS

not sure for part b

10. A standard stop sign measures 30.00 inches from flat to flat. What is the side length, x, of the stop

sign (to the nearest 0.01 in.)? Justify your answer.

30.00 in

Answers

Answer:

The answer is "12.426 in".

Step-by-step explanation:

[tex]\to b+2c=30\\\\\to b = 15 \times \tan 22.5 \\\\[/tex]

[tex]= 15 \times 0.414213562\\\\=6.21320343 \times 2 \\\\=12.4264069 \ in \\\\[/tex]

What is the meaning of a sample in mathematics?

Answers

Answer:

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.

Step-by-step explanation:

A tree cast a shadow of 10 ft when the suns rays hit the ground at an angle of elevation of 28 .what is the height of the tree ? Round your answer to the nearest tenth

Answers

Answer:

crcrc4cc4crfc

Step-by-step explanation:

Answer:

You can use scale factor

Step-by-step explanation:

Please help me I don’t know what to do

Answers

Look at the angles and the little tallies to match up the triangle. Or use the given: triangle DEF is similar to triangle KJI. If it’s like that in a given you know the order is equal. (D and K are similar, E and J, and F and I)
So if line FD is the 3rd and 1st letters of the first triangle, then it has to be equal to the 3rd and 1st letter of the 2nd triangle.
IK

Another way to do this is that when you find FD on the triangle you can set that the line has 3 tally marks. Then look at the other triangle and find a line in which there are 3 tally marks.
The order in which you put the letters does not matter. IK and KI should both be considered correct
Hope this helped

pls help.....

.....20 points

Answers

Answer:

Step-by-step explanation:

The simplest way to do this is to take every integer on there and divide it by 3.

8961/3 = 2987

5233/3 = 1744 1/3

10245/3 = 3415

-5469/3 = -1823

Because B does not produce an integer, that is your answer

(This works because of inverse operations)

Please let me know if you have any questions.

Dilate point a in relation to the origin by a dilation factor of 5.?

Answers

Answer:

origin dilation if 5. is 5

Our teacher hasn’t explained the concept yet but class was canceled today

Answers

Answer:

What grade is this?

Step-by-step explanation:

Solve for value the two angles in the triangle and classify the triangle using the sides and angles

Answers

Step-by-step explanation:

x + 15 +2x + 66 = 180

3x + 81 = 180

3x = 99

x = 99/3 = 33

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.

Answer:

The angles are 66, 66, and 48 degrees

The triangle is isosceles because 2 angles are equal, thus two leg lengths are equal

Step-by-step explanation:

the sum of all three angles in a triangle = 180 degrees

66 + 2x + (x+15) = 180

simplify

66 +3x + 15 = 180

reduce

81 + 3x = 180

subtract 81 from each side

81 - 81 + 3x = 180 - 81

3x = 99

divide both sides by 3

3x/3 = 99/3

x = 33

The length of a rectangle is three meters more than its width the perimeter of the rectangle is 74 meters what are the dimensions of the rectangle

Answers

Answer:

17 meters x 20 meters

Step-by-step explanation:

perimeter = 2 widths + 2 lengths

74 = 2W + 2L

L = W + 3

substitute for L

74 = 2W + 2(W + 3)

74 = 4W + 6

68 = 4W

W = 17 meters

L = 20 meters

Answer:

Step-by-step explanation:

Givens

Let the width = w

Then the Length = w + 3

Formula

P = 2L + 2W

P = 74

Solution

Substitute w + 3 for L

2(W + 3) + 2W = 74 Remove the brackets

2W + 6 + 2W = 74 Collect Like Terms

4w + 6 = 74 Subtract 6 from both sides

4w = 74 - 6

4w = 68 Divide by 4

w = 68/4

w = 17

L = w + 3

L = 17 + 3

L = 20

Check

P = 40 + 34

P =74

Help ASAP I’ll give you brainlest

Answers

Answer:

5.33 OR 5 1/3

Step-by-step explanation:

3 x 2³ ÷ 2 x 4 -1 +2

3 x 8 ÷ 2 x 4 -1 + 2

24 ÷ 8 +1

24 ÷ 9

2.66 OR 2 2/3

What is the area of a square with side length:

3cm

Answers

Answer:

Since every square has the same length in sizes...

3 x 3 = 9cm

Answer: 9cm

12cm :) the reason why it’s 12 is because a square has 4 sides so 3 by 4 is 12

Line c has a slope of 6/5. Line d is parallel to line c. What is the slope of line d?

Answers

Answer:

6/5

Step-by-step explanation:

Parallel lines have same slopes.

i need help with the work and math

Answers

What do you need help with ??

Solve for x : 80 + x = 100 - 14

Answers

Answer:

x=6

Step-by-step explanation:

100-14=86

86-80=6

Given: - 4x/7 > 10. Choose the solution set. {x | x < - } {x | x > - } {x | x > - } {x | x < - }

Answers

Answer:

{x | x < - 35 / 2}

Step-by-step explanation:

-4x / 7 > 10

Multiply both sides by 7

-4x /7 * 7 > 10 * 7

-4x > 70

Divide both sides by - 4

-4x / - 4 > 70 / - 4

x < - 35 / 2 (inequality sign changes)

100% of 100 is ?
100% of 8 is ?
100% of 24 is ?
100% of 36 is ?
100% of ¼ is ?

Answers

Answer:

100

1/4

Step-by-step explanation:

Answer:

100

1/4

Step-by-step explanation:

Find the area of the triangle.

Answers

answer: 28

explanation: a= 8(7)/2 = 28

hope this helps :)

BC =
Round your answer to the nearest hundredth.
B
?
65
А
7

Answers

Answer:

14 = rounded 15

Step-by-step explanation:

What grade r u in?

And what time is where u r?

Answer: 5.52 (answer already rounded)

Step-by-step explanation:

Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?

Answers

2(2) + 3(3) =

4 + 9 = 13

I don't know what 90p means but basically, u have to multiply that by 3 and add it to our current total which is 13.

Then, u substract the total cost from the 20 and you should get the change.

7 + a/3 = 5
PLS HELP ME
I've been siting here for 3 hours trying to figure this out.

Answers

Answer:

A=-6 is the answer

Step-by-step explanation:

it's simple

a = -6

7 + -6/3 = 5
7 + (-2) = 5

Hope this helps!!!!!

Which equation is the result of adding theses two equations -2x+4y=17 3x-10y=-3

Answers

Answer:

x=-79/4, y=-45/8. (-79/4, -45/8).

Step-by-step explanation:

-2x+4y=17

3x-10y=-3

---------------

3(-2x+4y)=3(17)

2(3x-10y)=2(-3)

----------------------

-6x+12y=51

6x-20y=-6

------------------

-8y=45

y=45/-8=-45/8

3x-10(-45/8)=-3

3x+450/8=-3

3x+225/4=-3

3x=-3-225/4

3x=-12/4-225/4

3x=-237/4

x=(-237/4)/3

x=(-237/4)(1/3)

x=-237/12=-79/4

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