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.
Function | Maclaurin Series |
sin(x) | |
cos(x) | |
tan(x) | |
sec(x) | |
eˣ | |
Geometric series 1 | |
Geometric series 2 | |
Geometric series 3 |
Example
This Maclaurin series has a clear pattern of
cos(x) Maclaurin series:In this case, it's:
So we could convert the series back to the trig function:
Example
Example
Looks quite a complicated series, but we look at the
factorial dominators, we found that resembles the pattern of thesin(x)'s maclaurin series.By comparing to the
sin(x) maclaurin series, we notice thatx = π/2, and all the rest are the same.So rewrite the series to the function:
And we get the result is
1.
Example
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