\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{x^2-3x+2}+x-4\right)=\lim\limits_{x\rightarrow-\infty}\left(\dfrac{-3x+2}{\sqrt{x^2-3x+2}-x}-4\right)\)
\(=\lim\limits_{x\rightarrow-\infty}\left(\dfrac{-3+\dfrac{2}{x}}{-\sqrt{1-\dfrac{3}{x}+\dfrac{2}{x^2}}-1}-4\right)=\dfrac{-3}{-2}-4=-\dfrac{5}{2}\)
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) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-2x+4}-x}{3x-1}\)
Tính:
\(\lim\limits_{x->-\text{oo}}\dfrac{\left(x-1\right)\left(x+2\right)}{x^2+9}\)
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 các giới hạn
a) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x+\sqrt{x^2+x-10}}{2x+3}\)
b) \(\lim\limits_{x\rightarrow+\infty}\dfrac{3x^2+\sqrt{x^2+x-10}}{\sqrt{x^3+x^2-3x-x^2+3}}\)
tính \(\lim\limits_{x\rightarrow2}=\dfrac{\sqrt{x-1}+x^4-3x^3+x^2+3}{\sqrt{2x}-2}\)
Tìm giới hạn:
a, \(\lim\limits_{x\rightarrow2}\dfrac{1-\sqrt{x^2+3}}{-x^2+3x-2}\)
b, \(\lim\limits_{x\rightarrow2}\dfrac{\sqrt{4x-1}+3}{x^2-4}\)
Các bạn tính giúp mình mấy câu này với:
1. \(\lim\limits_{x\rightarrow\left(-1\right)-}\dfrac{\sqrt{x^2-3x-4}}{1-x^2}\)
2. \(\lim\limits_{x\rightarrow2^+}\left(\dfrac{1}{x-2}-\dfrac{x+1}{\sqrt{x+2}-2}\right)\)
3. \(\lim\limits_{x\rightarrow+\infty}\dfrac{3x^2-5sin2x+7cos^2x}{2x^2+2}\)
4. \(\lim\limits_{x\rightarrow+\infty}\left(x.sin\left(\dfrac{1}{3x}\right)\right)\)
5. \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{2x+1}.\sqrt[3]{3x+1}.\sqrt[4]{4x+1}-1}{x}\)
6. \(\lim\limits_{x\rightarrow0}\left(\dfrac{\sqrt{9x+4}-\sqrt[3]{4x^{^2}+8}}{sinx}\right)\)
Tính các giới hạn
a) \(\lim\limits_{x\rightarrow+\infty}\sqrt[3]{x^3+3x^2}-\sqrt{x^2-2x}\)
b) \(\lim\limits_{x\rightarrow+\infty}\sqrt[n]{\left(x+a_1\right)\left(x+a_2\right)...\left(x+a_n\right)}-x\)
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) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt[3]{1+x^4+x^6}}{\sqrt{1+x^3+x^4}}\)
