# 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.

## 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:

Solve:

## Example

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:

• And we get the result is 1.