Maclaurin Series of Common functions

Maclaurin Series of Common functions

?Refer to Wiki: List of Maclaurin series of some common functions

Maclaurin series of these common functions are very useful, which we really want to memorize.

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Example

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Solve:

  • This Maclaurin series has a clear pattern of cos(x) Maclaurin series:

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  • In this case, it?s:

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  • So we could convert the series back to the trig function:

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Example

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Solve:

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Example

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Solve:

  • Looks quite a complicated series, but we look at the factorial dominators, we found that resembles the pattern of the sin(x)’s maclaurin series.
  • By comparing to the sin(x) maclaurin series, we notice that x = ?/2, and all the rest are the same.
  • So rewrite the series to the function:

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  • And we get the result is 1.

Example

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1

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