Find 1st 4 Non-Zero Terms Maclaurin Series

[pan angel]

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

 

[relinquished™]

I believe the the Maclaurin Series is given by the equation

$$<br /> f(x) = f(0) + f'(0)x + \frac{f''(0)x^2}{2!} + \frac{f'''(0)x^3}{3!} + \frac{f^(4) (0)x^4}{4!} + ... + \frac{f^(n) (0)x^n}{n!} + ...<br />$$

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.

 

[josephcollins]

the first four non-zero terms will then be for those terms for which fn(0) is not zero.

 

[relinquished™]

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