\(=\lim\limits_{x\rightarrow+\infty}\frac{\frac{1}{x}-1}{x-6+\frac{2}{x}}=\frac{-1}{+\infty}=0\)
\(=\lim\limits_{x\rightarrow+\infty}\frac{\frac{1}{x}-1}{x-6+\frac{2}{x}}=\frac{-1}{+\infty}=0\)
\(\lim\limits_{x\rightarrow0}\left(\frac{1}{x}+\frac{1}{x^2}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\frac{\sqrt{\left(-x\right)^2+2}}{x-1}\)
\(\lim\limits_{x\rightarrow-\infty}\frac{|x|+\sqrt{x^2+x}}{x+10}\)
Tính các giới hạn
a) \(\lim\limits_{x\rightarrow\infty}\sqrt{2x^2+x-2}-x\)
b) \(\lim\limits_{x\rightarrow-\infty}\sqrt{x^2+x-2}+x\)
Tính giới hạn
a) \(\lim\limits_{x\rightarrow-\infty}\dfrac{x+3}{3x-1}=\dfrac{1}{3}\)
b) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-2x+4}-x}{3x-1}\)
Tính: \(\lim\limits_{x\rightarrow-\infty}\sqrt[3]{-8x^5+6x^3+2}\)
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 các giới hạn
a) \(\lim\limits_{x\rightarrow-\infty}\dfrac{x+3}{3x-1}\)
b) \(\lim\limits_{x\rightarrow+\infty}\dfrac{\left(\sqrt{x^2+1}+x\right)^n-\left(\sqrt{x^2+1}-x\right)^n}{x}\)
Tính các giới hạn
a) \(\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt[3]{x^3+2x^2-4x+1}}{\sqrt{2x^2+x-8}}\)
b) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-2x+4}-x}{3x-1}\)
Tính giới hạn
a) \(\lim\limits_{x\rightarrow4^-}\dfrac{2x-5}{x-4}=-\infty\)
b) \(\lim\limits_{x\rightarrow+\infty}\left(-x^3+x^2-2x+1\right)\)
Tìm giới hạn:
a, \(\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt{x^2+x+2}}{x-1}\)
b, \(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{4x^2-x}+2x\right)\)