TrinhVietLinh

$\lim_{x->3}(\frac{2\sqrt{x+6}+5\sqrt[3]{x-2}{-11}}{2x-6}) =\lim_{x \mapsto 3 }(\frac{\sqrt{4x+24}+\sqrt[3]{125x-250}-11}{2x-6}) =\lim_{x \mapsto 3}(\frac{\sqrt{4x+24}-6-5+\sqrt[3]{125x-250}}{2x-6}) =\lim_{x \mapsto 3}(\frac{\sqrt{4x+24}-6}{2x-6})+\lim_{x \mapsto 3}(\frac{\sqrt[3]{125x-250}-5}{2x-6}) =\lim_{x \mapsto 3}(\frac{4x-12}{(2x-6)(\sqrt{4x+24}+6)}+\lim_{x \mapsto 3}(\frac{125x-375}{(2x-6)(\sqrt[3]{125x-250}^{2}+5\sqrt[3]{125x-250}+25)}) =\lim_{x \mapsto 3}(\frac{2}{\sqrt{4x+24}+6})+\lim_{x \mapsto 3}(\frac{125}{2(\sqrt[3]{125x-250}^{2}+5\sqrt[3]{125x-250}+25)}) =\frac{1}{6}+\frac{5}{6}=1$