## maclaurin series

Im helping my sis study for her exam but i can't remember how to find the first four non-zero terms of the maclaurin series

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 I believe the the Maclaurin Series is given by the equation $$f(x) = f(0) + f'(0)x + \frac{f''(0)x^2}{2!} + \frac{f'''(0)x^3}{3!} + \frac{f^(4) (0)x^4}{4!} + ... + \frac{f^(n) (0)x^n}{n!} + ...$$ So in order for you to know the first four terms of the series, you need to know what $$f(a), f'(a), f''(a)$$ and $$f'''(a)$$ and then plug in a=0 in their respective formulas/equations. Then just plug them in the equation of the Maclaruin Series. Hope this helps.
 the first four non-zero terms will then be for those terms for which fn(0) is not zero.

## maclaurin series

Oh yeah, forgot about that. When using the formula, if any of the terms you encounter are zero, you must proceed to the next and check if it is non-zero. Ex: If $$f''(0) = 0$$ then you must proceed and check whether $$f'''(0) = 0$$ and so on