Olá
oi,não entendi direito suas contas.
\(\lim_{ h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\)
então:
\(\lim_{ h \rightarrow 0} \frac{\sqrt{3-x-h}-\sqrt{3-x}}{h}\)
\(\lim_{ h \rightarrow 0} \frac{(\sqrt{3-x-h}-\sqrt{3-x})*(\sqrt{3-x-h}+\sqrt{3-x})}{h(\sqrt{3-x-h}+\sqrt{3-x})}\)
\(\lim_{ h \rightarrow 0} \frac{3-x-h-(3-x)}{h(\sqrt{3-x-h}+\sqrt{3-x})}\)
\(\lim_{ h \rightarrow 0} \frac{3-x-h-3+x}{h(\sqrt{3-x-h}+\sqrt{3-x})}\)
\(\lim_{ h \rightarrow 0} \frac{-h}{h(\sqrt{3-x-h}+\sqrt{3-x})}\)
\(-\lim_{ h \rightarrow 0} \frac{h}{h(\sqrt{3-x-h}+\sqrt{3-x})}\)
\(-\lim_{ h \rightarrow 0} \frac{1}{\sqrt{3-x-h}+\sqrt{3-x}}\)
\(-\frac{1}{\sqrt{3-x}+\sqrt{3-x}}\)
\(-\frac{1}{2\sqrt{3-x}}\)
Agora aplicando no ponto \(x=2\)
\(-\frac{1}{2\sqrt{3-2}}=-\frac{1}{2}\)