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\begin{aligned}\mathrm{m}_{\tan } &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{(x+h)-(x)}=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-(x)^{2}}{(x+h)-(x)}=\lim _{h \rightarrow 0} \frac{x^{2}+2 x h+h^{2}-x^{2}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 x h+h^{2}}{h}=\lim _{h \rightarrow 0} \frac{h(2 x+h)}{h}=\lim _{h \rightarrow 0}(2 x+h)=\mathbf{2} \mathbf{x}\end{aligned}