Taylor Polynomial

A way to upgrade linear approximation to higher order approximations.

A taylor polynomial centered at $x_0=0$ is considered a maclaurin polynomial

Shortcuts

Utilizing maclaurin’s theorem, we have the following shortcuts: Subbing in another term for the taylor polynomial will give you the taylor polynomial for that same term in f(x)

includes quadratic approximation, cubic approximation, Higher order approximation

Next: Taylor’s Inequality