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# Power Series watch

1. Was wondering if anyone could explain how to get the power series for a function up to x^3

For example sinx

Cheers
2. Use Taylors Theorem :

Suppose you want to expand about x = a

Typically you expand about x=0 so this becomes

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

Therefore

3. (Original post by AlphaNumeric)
4. (Original post by C4>O7)
My terminology was correct. If you are expanding about x=b, then a=b. In this case, if you expand about x=0, then a=0. The value of a is a consequence of the point you are expanding about.

It is much of a muchness, since either way you set a=0

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