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
Aliun [14]
3 years ago
8

Write the Taylor Series for f(x) = sin(x)center

Mathematics
1 answer:
tangare [24]3 years ago
3 0

Answer:

Taylor series of sin(x) centered at x = 0.

Step-by-step explanation:

Taylor series expansion:

\sum_{n=0}^N f^n(a)\displaystyle\frac{(x-a)^n}{n!}

Here, f(x) = sin (x) and a = 0

f(x) = \sin x, f(0) = 0\\f'(x) = \cos x, f'(0) = 1\\f''(x) = -\sin x, f''(0) = 0\\f'''(x) = -\cos x, f'''(0) = -1\\f^4(x) = \sin x, f^4(0) = 0\\f^5(x) = \cos x, f^5(0) = 0

Putting all the values and expanding, we get,

f(x) = f(a) + \displaystyle\frac{f'(a)(x-a)}{1!} + \displaystyle\frac{f''(a)(x-a)^2}{2!} + \displaystyle\frac{f'''(a)(x-a)^3}{3!} + \displaystyle\frac{f^4(a)(x-a)^4}{4!} + \displaystyle\frac{f^5(a)(x-a)^5}{5!} + ...\\\\= \sin 0 + \displaystyle\frac{x}{1!} +  \displaystyle\frac{(0)x^2}{2!} + \displaystyle\frac{(-1)x^3}{3!} + \displaystyle\frac{(0)x^4}{4!} + \displaystyle\frac{(1)x^5}{5!} + ...

Solving, we get

\sin x = x - \displaystyle\frac{x^3}{3!} + \displaystyle\frac{x^5}{5!} - \displaystyle\frac{x^7}{7!} + ...\\\\\sin x = x - \displaystyle\frac{x^3}{6} + \displaystyle\frac{x^5}{120} - \displaystyle\frac{x^7}{5040} + ...

You might be interested in
Which line plot displays a data set with an outlier? An untitled line plot from 10 to 21. The plot displays the following values
RSB [31]

Answer:

Is there a picture because I don’t know what you need help with you typed a lot of words but not a picture

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What shape can be created by the given net? triangular pyramid wedge triangular prism cone
Juliette [100K]

Answer:

triangular prism

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Plz help i will give brainly
joja [24]

Answer:

Step-by-step explanation:

3rd

5 0
3 years ago
Read 2 more answers
Betty's height is 2/3 of Jinlan's height. Find the ratio of Betty's height to Jinlan's height.
nasty-shy [4]
Betty's height versus Jinlan's height is 2:3
3 0
2 years ago
IM SO BORED I’m in the car with absolutely nothing to do please help me
s344n2d4d5 [400]

Answer: F

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • Let → a = ⟨ 1 , − 3 ⟩ and → b = ⟨ − 3 , k ⟩. Find k so that →a and → b will be orthogonal (form a 90 degree angle).
    13·1 answer
  • 5) If f(x)=x2-x, what is f(-5)?<br> A. -30<br> B. -20<br> C. 20<br> D. 30
    7·1 answer
  • Solve -4x+y=8 and 2x=-y-10
    6·1 answer
  • Arnold purchased 3 apples at the store for $3.90. This weekhe purchased 5 apples for $6.50. Help Arnold analyze the priceof appl
    7·1 answer
  • 3/7 of the people who live in the apartment building are men. 5/8 of the remaining people are women. The rest are children. a to
    15·1 answer
  • Classify the following triangle as right, acute or obtuse using the following side measurements: 20cm, 12cm, 16cm
    6·1 answer
  • I will mark you brainiest if you can answer this
    13·1 answer
  • 17 students on the math team want to raise 483.62 to buy practice books they have already raised 218.25 if each students raises
    11·1 answer
  • Which 2 number have the mean of 10 and range of 4
    11·1 answer
  • When asked to explain why there is no solution to |3x+7|-5 Jack said, "It is not a solution because the 5 is negative." Jack is
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!