Đáp án:$\lim_{x\to1}\dfrac{\sqrt[3]{5x+3}-2}{x-1}=\dfrac5{12}$
Giải thích các bước giải:
$\lim_{x\to1}\dfrac{\sqrt[3]{5x+3}-2}{x-1}$
$=\lim_{x\to1}\dfrac{\dfrac{5x+3-2^3}{\sqrt[3]{5x+3}^2+2\sqrt[3]{5x+3}+4}}{x-1}$
$=\lim_{x\to1}\dfrac{\dfrac{5(x-1)}{\sqrt[3]{5x+3}^2+2\sqrt[3]{5x+3}+4}}{x-1}$
$=\lim_{x\to1}\dfrac{5}{\sqrt[3]{5x+3}^2+2\sqrt[3]{5x+3}+4}$
$=\dfrac{5}{\sqrt[3]{5\cdot1+3}^2+2\sqrt[3]{5\cdot1+3}+4}$
$=\dfrac5{12}$