Let us consider the function defined by
[![function defined by ][1]][1]
We have f(0)=0 How we show that f(x) is not equal to it's Taylor expansion at x=O
I try to get coefficients,
$c_0 = 0$,
$c_1= $
[1]: https://i.stack.imgur.com/MDeRD.jpg unable to find this limit, please tell me how i prove this...
You can show that $$f^{(n)}(0)=0$$
which means that the Taylor expansion of $f$ at $x=0$ is
$$\sum_{n=0}^\infty f^{(n)}\frac{x^n}{n!} = \sum_{n=0}^\infty 0 = 0$$
and $0$ (the Taylor expansion of $f$) is clearly not equal to $f$.