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![\bf \stackrel{\textit{de} \textit{finition of a derivative as a limit}}{\lim\limits_{h\to 0}~\cfrac{f(x+h)-f(x)}{h}}\\\\ -------------------------------\\\\ f(x)=2x^2+1\implies \lim\limits_{h\to 0}~\cfrac{[2(x+h)^2+1]~~-~~[2x^2+1]}{h} \\\\\\ \lim\limits_{h\to 0}~\cfrac{[2(x^2+2xh+h^2)+1]~~-~~[2x^2+1]}{h} \\\\\\ \lim\limits_{h\to 0}~\cfrac{[2x^2+4xh+2h^2+1]~~-~~[2x^2+1]}{h}](/tpl/images/0094/0640/7f537.png)
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F(x)=2x^2+1 using the derivate definition...
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