Tìm các giới hạn sau:
\(\lim\limits_{x\rightarrow-\infty}\) \(\dfrac{\sqrt{x^6+2}}{3\text{x}^3-1}\)
\(\lim\limits_{x\rightarrow+\infty}\) \(\dfrac{\sqrt{x^6+2}}{3\text{x}^3-1}\)
\(\lim\limits_{x\rightarrow-\infty}\) \(\left(\sqrt{2\text{x}^2+1}+x\right)\)
\(\lim\limits_{x\rightarrow1}\) \(\dfrac{2\text{x}^3-5\text{x}-4}{\left(x+1\right)^2}\)
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) \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{4x^2-3x+1}-2x\right)\)
1) Tính giới hạn \(\lim\limits_{n\rightarrow\infty}\dfrac{-n^2+2n+1}{\sqrt{3n^4+2}}\)
2) Tính giới hạn \(\lim\limits_{n\rightarrow\infty}\left(\dfrac{4n-\sqrt{16n^2+1}}{n+1}\right)\)
3) Tính giới hạn \(\lim\limits_{n\rightarrow\infty}\left(\dfrac{\sqrt{9n^2+n+1}-3n}{2n}\right)\)
tính giới hạn
a) \(\lim\limits_{x\rightarrow+\infty}\dfrac{5x^2+x^3+5}{4x^3+1}\)
b) \(\lim\limits_{x\rightarrow-\infty}\dfrac{2x^2-x+1}{x^3+x-2x^2}\)
c) \(\lim\limits_{x\rightarrow-\infty}\dfrac{2x^2-x+1}{x^3+x-2x^2}\)
a) \(\lim\limits_{x\rightarrow+\infty}\)\(^{3_{\sqrt{x^3+4x^2}-x}}\)
b) \(f\left(x\right)=\left\{{}\begin{matrix}\dfrac{4x-1}{x-1}neux>1\\7x+1neux< 1\end{matrix}\right.\)
Tính \(\lim\limits f\left(x\right)_{x\rightarrow1^+}\) , \(\lim\limits f\left(x\right)_{x\rightarrow1^-}\)
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) \(\lim\limits_{x->+\infty}\left(3_{\sqrt{x^3+4x^2}-x}\right)\)
1) Tính giới hạn \(\lim\limits_{n\rightarrow\infty}\left(\dfrac{3^n-4^{n+1}}{3^{n+2}+4^n}\right)\)
2) Tính giới hạn \(\lim\limits_{n\rightarrow\infty}\left(\dfrac{3^n-4.2^{n+1}-3}{3.2^n+4^n}\right)\)
3) Tính giới hạn \(\lim\limits_{n\rightarrow\infty}\left(\dfrac{2-5^{n-2}}{3^n+2.5^n}\right)\)
cho hàm số \(y=f\left(x\right)\) liên tục trên R thỏa
\(\lim\limits_{x\rightarrow-\infty}f\left(x\right)=+\infty\) , \(\lim\limits_{x\rightarrow+\infty}f\left(x\right)=-\dfrac{1}{2}\)
tìm số đường tiệm cận củ đồ thị hàm số đã cho
\(\lim\limits_{x\rightarrow-\infty}f\left(x\right)=+\infty\)
Tính các giới hạn sau :
1/\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{4x^2-3x+1}+2x\right)\)
2/\(lim\left(\sqrt{4n^2+2n+1}-2n+2020\right)\)
