1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
iren2701 [21]
3 years ago
14

Find the expansion of cos x about the point x=0

Mathematics
1 answer:
ycow [4]3 years ago
8 0

Answer:

Cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{1!} + ...

Step-by-step explanation:

We use Taylor series expansion to answer this question.

We have to find the expansion of cos x at x = 0

f(x) = cos x, f'(x) = -sin x, f''(x) = -cos x, f'''(x) = sin x, f''''(x) = cos x

Now we evaluate them at x = 0.

f(0) = 1, f'(0) = 0, f''(0) = -1, f'''(0) = 0, f''''(0) = 1

Now, by Taylor series expansion we have

f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)(x-a)^2}{2!} + \frac{f'''(a)(x-a)^3}{3!} + \frac{f''''(a)(x-a)^4}{4!} + ...

Putting a = 0 and all the values from above in the expansion, we get,

Cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{1!} + ...

You might be interested in
Last year, sales at a book store increased from $5,000 to $10,000. This year, sales decreased to $5,000 from $10,000. What perce
Grace [21]
Increased 100%, decreased 50%
4 0
3 years ago
Read 2 more answers
Sara is building a circular garden with a radius of 14 m. She can buy the fencing in
mojhsa [17]

Answer:

she need to buy 9 packs

Step-by-step explanation:

C = 2πr

= 2·3.14·14

= 87.92 m

she need to buy 9 packs

5 0
3 years ago
Read 2 more answers
Bovine deposits $7,000 into an investment that pays 4% interest compounded quarterly. if she leaves it in the account for 9 year
inysia [295]

Answer:

her balance will be $7,560 after 9 years i believe.

Step-by-step explanation:


4 0
3 years ago
What is the area of the triangle?<br> 6<br> 2<br> 3
Llana [10]

Answer:

6

Step-by-step explanation:

Find the area of both triangles inside the bigger triangle and add them together.

Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:

a² + b² = c²

2² + b² = 3²

4 + b² = 9

5 = b²

2.2 ≈ b

Calculate the area of the smaller triangle:

1/2(bxh)

1/2(2 x 2.2)

1/2(4.4)

2.2

Calculate the area of the bigger triangle:

<em>We know that the longer leg is 3.8 units because we were able to subtract the length of the smaller triangle's leg from 6. </em>

1/2(bxh)

1/2(2 x 3.8)

1/2(7.6)

3.8

Add both areas to find the area of the largest triangle:

3.8 + 2.2 = 6

7 0
3 years ago
What is the square root of 100
tino4ka555 [31]
I believe that the answer to the equation is 10
8 0
2 years ago
Other questions:
  • In how many ways can 7 distinct red balls and 5 distinct blue balls be placed in a row such that all red balls are adjacent,
    12·1 answer
  • A candidate for mayor plans to campaign at 5 shopping malls before the election. In how many different ways can the candidate sc
    13·1 answer
  • What is the value of n in math
    5·2 answers
  • Help it’s algebra 2!! asap plzz
    12·1 answer
  • What is the answer to this problem please -5a +3(3a -9)=
    8·1 answer
  • Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
    8·1 answer
  • ILL GIVE BRAINLY!!!<br> find y. Give your answer in the simplest form
    12·1 answer
  • What percentage of a dollar is the value of 5 quarters and 1 dime
    6·1 answer
  • What is the answer to 6a + 6c =126
    15·1 answer
  • What is the answer for this question above
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!