\(\lim\limits_{x\rightarrow+\infty}\left(x-\sqrt{x^2+3x}\right)=\lim\limits_{x\rightarrow+\infty}\dfrac{\left(x-\sqrt{x^2+3x}\right)\left(x+\sqrt{x^2+3x}\right)}{x+\sqrt{x^2+3x}}\)
\(=\lim\limits_{x\rightarrow+\infty}\dfrac{-3x}{x+\sqrt{x^2+3x}}=\lim\limits_{x\rightarrow+\infty}\dfrac{-3}{1+\sqrt{1+\dfrac{3}{x}}}=-\dfrac{3}{2}\)
tính giới hạn
a) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x+1}{x^2+x+1}\)
b) \(\lim\limits_{x\rightarrow+\infty}\dfrac{3x+1}{3x^2-x+5}\)
c) \(\lim\limits_{x\rightarrow-\infty}\dfrac{3x+5}{\sqrt{x^2+x}}\)
d) \(\lim\limits_{x\rightarrow+\infty}\dfrac{-5x+1}{\sqrt{3x^2+1}}\)
tính giới hạn
a) \(\lim\limits_{x\rightarrow+\infty}\left(2x-\sqrt{x^2+4x-3}\right)\)
b) \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{4x^2-3x+1}-2x\right)\)
Tìm các giới hạn sau:
\(\lim\limits_{x\rightarrow-\infty}\) \(\dfrac{\sqrt{x^6+2}}{3\text{x}^3-1}\)
\(\lim\limits_{x\rightarrow+\infty}\) \(\dfrac{\sqrt{x^6+2}}{3\text{x}^3-1}\)
\(\lim\limits_{x\rightarrow-\infty}\) \(\left(\sqrt{2\text{x}^2+1}+x\right)\)
\(\lim\limits_{x\rightarrow1}\) \(\dfrac{2\text{x}^3-5\text{x}-4}{\left(x+1\right)^2}\)
Giúp mình với ạ
1) lim\(\dfrac{3x^2+5}{x^3-x+2}\)(x-->+∞)
2) lim\(\dfrac{2x^2\left(3x^2-5\right)^3\left(1-x\right)^5}{3x^{14}+x^2-1}\)(x-->-∞)
3) lim\(\dfrac{3x-\sqrt{2x^2+5}}{x^2-4}\)(x-->+∞)
Tính lim \(\left(x\rightarrow-\infty\right)\)\(\sqrt{3x^2-2x+1}\)
1) lim \(\frac{-x^2+3x}{x^3-2x^2+x}\) (x->1)
2) lim \(\frac{\sqrt{1+2x}-\sqrt[3]{1+3x}}{x^2}\) (x->0)
3) lim \(\frac{x\sqrt[3]{x^3+1
}}{2-x\sqrt{1+4x^2}}\) (x-> âm vô cùng )
4) lim \(\frac{\cos^9x-1}{x}\) (x->0)
giúp mình với ạ
Tính các giới hạn sau :
1/\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{4x^2-3x+1}+2x\right)\)
2/\(lim\left(\sqrt{4n^2+2n+1}-2n+2020\right)\)
11) \(\lim\limits_{x->1}\) \(\dfrac{3_{\sqrt{4x-1}-\sqrt{4x-3}}}{x-1}\)
11) \(\lim\limits_{x->4}\dfrac{4x-1}{x^2-8x+16}\)
12) \(\lim\limits_{x->2}\)\(\dfrac{4-x^2}{x^3-8}\)
13) \(\lim\limits_{x->+\infty}\left(3_{\sqrt{x^3+4x^2}-x}\right)\)
Tính lim \(\left(x\rightarrow+\infty\right)\dfrac{x\sqrt{x}+x+1}{x^2+x+10}\)
