Maclaurin Series of Common functions
Published in
2 min readJan 17, 2019
►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.
Example
Solve:
- 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
Solve:
Example
Solve:
- 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
