# Thread: Proving Maclaurin series function

1. ## Proving Maclaurin series function

Show that the function defined by

is not equal to its Maclaurin series.

2. Originally Posted by racewithferrari
Show that the function defined by

is not equal to its Maclaurin series.
You have to show that $f^{(k)}(0)=0$, for all $k\in \mathbb{N}$, so that the Maclaurin series is identical to 0, for all $x\in\mathbb{R}$, but $f(x)\neq 0$, for all $x\in \mathbb{R}\backslash\{0\}$.