\(\lim\limits_{x\to-\infty}\frac{x^4+2x^3+x-1}{x^2+3x-1}=\lim\limits_{x\to-\infty}\frac{x^2\left(x^2+3x-1\right)-x\left(x^2+3x-1\right)+4x^2-1}{x^2+3x-1}\)
\(\lim\limits_{x\to-\infty}\left(x^2-x+\frac{4x^2-1}{x^2+3x-1}\right)=\lim\limits_{x\to-\infty}\left(x^2-x+\frac{4-\frac{1}{x^2}}{1+\frac{3}{x}-\frac{1}{x^2}}\right)=\lim\limits_{x\to-\infty}\left(x^2-x\right)+4=+\infty\)
Tính giới hạn
a) \(\lim\limits_{x\rightarrow-\infty}\dfrac{x+3}{3x-1}=\dfrac{1}{3}\)
b) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-2x+4}-x}{3x-1}\)
tìm giới hạn \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{4x^2+2x-1}-x}{3x-2}\)
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) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-2x+4}-x}{3x-1}\)
tìm giới hạn
\(\lim\limits_{x\rightarrow-\infty}\frac{x^2-3x-2}{x^3+2x+1}\)
Tính các giới hạn
a) \(\lim\limits_{x\rightarrow+\infty}\sqrt[3]{x^3+3x^2}-\sqrt{x^2-2x}\)
b) \(\lim\limits_{x\rightarrow+\infty}\sqrt[n]{\left(x+a_1\right)\left(x+a_2\right)...\left(x+a_n\right)}-x\)
tìm giới hạn
\(\lim\limits_{x\rightarrow-\infty}\frac{\sqrt{x^2+2x}+3x}{\sqrt{4x^2+1}-x+3}\)
Tính giới hạn
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{x^3+3x^2}-\sqrt{x^2-2x}\right)\)
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) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt[3]{1+x^4+x^6}}{\sqrt{1+x^3+x^4}}\)
7)Tính giới hạn:
\(a)\lim\limits_{x\rightarrow+\infty}x\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right)\)
\(b)\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{x^3+3x^2}-\sqrt{x^2-2x}\right)\)
