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"Prove that "lim(hrarr0) (f(x+h)+f(x-h)-...

`"Prove that "lim_(hrarr0) (f(x+h)+f(x-h)-2f(x))/(h^(2))=f''(x)" (without using L' Hospital's rule)".`

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To prove that \[ \lim_{h \to 0} \frac{f(x+h) + f(x-h) - 2f(x)}{h^2} = f''(x) \] we will follow a systematic approach without using L'Hôpital's rule. ...
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