Question about limits, derivative definition – math.stackexchange.com

I have MacLaurin series: $$f(x)=f(0)+f'(0) x+\frac12 f''(0)x^2+...$$ Suppose $$f(x)=c_0+c_1 x+c_2 x^2+o(x^3)$$as $x\to0$. Then I can show $c_0=f(0)$ and $c_1=f'(0)$. Then ...

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