\(\lim\limits_{x\rightarrow0}\frac{\left(2x+1\right)^{\frac{1}{2}}-\left(3x+1\right)^{\frac{1}{3}}}{x^2}=\lim\limits_{x\rightarrow0}\frac{\left(2x+1\right)^{-\frac{1}{2}}-\left(3x+1\right)^{-\frac{2}{3}}}{2x}\)
\(=\lim\limits_{x\rightarrow0}\frac{-\left(2x+1\right)^{-\frac{3}{2}}+2\left(3x+1\right)^{-\frac{5}{3}}}{2}=\frac{-1+2}{2}=\frac{1}{2}\)
Tính giới hạn sau:
\(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+2x}.\sqrt[3]{1+3x}-\sqrt{1+4x}}{1+x-\sqrt{1+2x}}\)
Tìm giới hạn: \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+2x}\sqrt[3]{1+3x}-1}{x}\)
Tìm giới hạn: \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+2x}\sqrt[3]{1+3x}\sqrt[4]{1+4x}-1}{x}\)
Tính các giới hạn
\(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{x^2+x+1}-\sqrt[3]{x^3+1}}{x}\)
Tính các giới hạn
a) \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{x+1}-\sqrt[3]{x-1}}{x}\)
b) \(\lim\limits_{x\rightarrow2}\dfrac{\sqrt[3]{x-3}+\sqrt[4]{2x-3}}{x-2}\)
Tính các giới hạn sau:
a) \(\lim\limits_{x\rightarrow0^-}\dfrac{2\left|x\right|+x}{x^2-x}\)
b) \(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{x^2-x}-\sqrt{x^2-1}\right)\)
c) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt[3]{1+x^4+x^6}}{\sqrt{1+x^3+x^4}}\)
tính \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+2x}-\sqrt[3]{1+3x}}{x^2}\)
Tìm giới hạn:
\(\lim\limits_{x\rightarrow0}\dfrac{2\sqrt{1+x}-\sqrt[3]{8-x}}{x}\)
\(\lim\limits_{x\rightarrow0}\frac{\sqrt{2x+1}-\sqrt[3]{3x+1}}{x^2}\)
