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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} + ...

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Answer:

The answer is 113.10 square meters. Calculate the area of 6 meter circle and you get 113.10. Have a great day!!!

Step-by-step explanation:

8 0
4 years ago
1). 3+(10)+6 <br> 2). (-3)+3+12<br> 3). (-3)-6<br> 4). 3-(-2)<br> 5). 5-3-(-2)<br> 6). 7-(-6)-7
Alika [10]

Answer:

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6 0
3 years ago
Let f(x) = 9x - 2 and g(x) = -x + 3. Find f(g(x)).<br><br> I think it's -9x-2
almond37 [142]
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8 0
4 years ago
The length of a 1-inch paperclip is about 1.6 x 10−5 miles. It takes about 1.5 x 1010 paperclips linked together to reach the mo
son4ous [18]

Answer:

Distance from the moon is 2.4 × 10⁵ miles

Step-by-step explanation:

Length of 1-inch paperclip = 1.6\times 10^{-5} miles

Number of paperclips used to reach the moon = 1.5 × 10¹⁰

Total distance from the moon = Number of paper clips used × Length of one clip

= (1.5 × 10¹⁰) × (1.6 × 10⁻5)

= (1.5 × 1.6) (10¹⁰× 10⁻⁵)

= 2.4 × 10⁽¹⁰⁻⁵⁾ miles

= 2.4 × 10⁵ miles

Distance from the moon is 2.4 × 10⁵ miles.

5 0
3 years ago
What is the answer to this problem
Romashka-Z-Leto [24]
Work:

     1355.4
    _____
5 | 6777 
  - 5000
 -----------
    1777
  - 1500
 ----------
      277
  -   250
 -----------
        27
  -     25
 -------------
          2.0
  -       2.0
---------------
              0

Answer:

1355.4   or   1355 remainder 2 (if you need remainder)

5 0
3 years ago
Read 2 more answers
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