Đáp án:
Giải thích các bước giải:
$\lim_{x \to 1}\frac{\sqrt[3]{5x +3}-\sqrt[]{x+3} }{x-1} $ = $\lim_{x \to 1}\frac{\sqrt[3]{5x +3} -2-\sqrt[]{x+3}+2}{x-1} $ = $\lim_{x\to 1}\frac{\sqrt[3]{5x +3}-2}{x-1} $ - $\lim_{x \to 1} \frac{\sqrt[]{x+3}-2}{x-1}$ = $\lim_{x \to 1}\frac{5x+3-8}{(x-1)((\sqrt[3]{5x+3})^2+2\sqrt[3]{5x +3}+4} $ - $\lim_{x \to 1}\frac{x+3-4}{(x-1)(\sqrt[]{x+3}+2)} $ = $\lim_{x \to 1}\frac{5}{(\sqrt[3]{5x+3})^2+2\sqrt[3]{5x +3}+4} $ - $\lim_{x \to 1}\frac{1}{\sqrt[]{x+3}+2} $ = $\frac{5}{12}$ -$\frac{1}{4}$ = $\frac{1}{6}$
