Find 1st 4 Non-Zero Terms Maclaurin Series

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Discussion Overview

The discussion revolves around finding the first four non-zero terms of the Maclaurin series for a function. It includes theoretical aspects of the series and practical steps for computation.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant seeks assistance in recalling how to find the first four non-zero terms of the Maclaurin series.
  • Another participant provides the general formula for the Maclaurin series, emphasizing the need to evaluate the function and its derivatives at zero.
  • It is noted that the first four non-zero terms depend on the derivatives at zero being non-zero.
  • A further clarification is made that if any derivative evaluated at zero is zero, one must check subsequent derivatives until finding non-zero values.

Areas of Agreement / Disagreement

Participants generally agree on the process of finding non-zero terms but do not reach a consensus on specific functions or examples to apply the method.

Contextual Notes

The discussion does not specify any particular function for which to find the Maclaurin series, leaving the context open to various applications.

pan angel
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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

[tex] <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 /> [/tex]

So in order for you to know the first four terms of the series, you need to know what [tex]f(a), f'(a), f''(a)[/tex] and [tex]f'''(a)[/tex] 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. :biggrin:
 
the first four non-zero terms will then be for those terms for which fn(0) is not zero.
 
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 [tex]f''(0) = 0[/tex] then you must proceed and check whether [tex]f'''(0) = 0[/tex] and so on
 

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