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

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 the sin(x)'s maclaurin series.

• By comparing to the sin(x) maclaurin series, we notice that x = π/2, and all the rest are the same.

• So rewrite the series to the function:

  

• And we get the result is 1.

Example

Solve: