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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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A farmer harvested some of his pecan crops on Friday and Saturday.what fraction of the pecan crop was harvested in two days
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Hence the 3.28 %or 2/61  of total work will be done .

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Given:

The pecan crops are harvested for  friday and saturday (2days)

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What fraction these 2 days corresponds to the harvesting days?

Solution;

The  pecan crops are growing in America  in state of Georgia

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