a/
\(lim\dfrac{\sqrt{n^2-n}-n}{n}=lim\dfrac{-n}{n\left(\sqrt{n^2-n}+n\right)}=lim\dfrac{-\dfrac{1}{n}}{1\left(\sqrt{1-\dfrac{1}{n}}+1\right)}=\dfrac{0}{2}=0\)
b/
\(lim\dfrac{2^n-5^{n+2}}{5^n-4^{2-n}}=lim\dfrac{8^n-25.20^n}{20^n-4^2}=lim\dfrac{\left(\dfrac{8}{20}\right)^n-25}{1-\dfrac{16}{20^n}}=\dfrac{0-25}{1-0}=-25\)
bài 1
a. \(\lim\limits_{n\rightarrow+\infty}\left(\sqrt[3]{n^3+3n+1}-n\right)\)
b. \(\lim\limits_{n\rightarrow+\infty}\left(\sqrt[3]{n^3+2n}-\sqrt{n^2+1}\right)\)
c.\(\lim\limits_{n\rightarrow+\infty}\left(\sqrt[3]{n^3+n}-\sqrt[3]{n^3-2n^2}\right)\)
bài 2
a. \(\lim\limits_{n\rightarrow+\infty}\left(2n-\sqrt{n^2+3n}\right)\)
b. \(\lim\limits_{n\rightarrow+\infty}\left(\sqrt{n^2+2}-\sqrt{3n+1}\right)\)
c. \(\lim\limits_{n\rightarrow+\infty}\left(n\sin2n-3n^3\right)\)
tính \(\lim\limits_{n\rightarrow+\infty}n\left(\sqrt{n^2-2n}-\sqrt[3]{n^3-3n^2}\right)\)
tìm giới hạn của dãy số
1.\(\lim\limits_{n->\infty}\left(\sqrt[3]{n^3+n^2+n+1}-n\right)\)
2.\(\lim\limits_{n->\infty}\left(\sqrt{n^2+n}-\sqrt{n^2-n+1}\right)\)
3.tìm a,b để \(\lim\limits_{n->\infty}\left(\sqrt{an^2+bn+2}-2n\right)=2\)
bài 1
a. \(\lim\limits_{n\rightarrow+\infty}\left(-n^6+7n+1\right)\)
b. \(\lim\limits_{n\rightarrow+\infty}\sqrt[3]{2n^3-n+1}\)
bài 2: Tính
a. \(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...\)
b. B= 1+0.1+0.01+0.001+0.0001+...
cho \(\lim\limits_{x\rightarrow-\infty}\dfrac{a\sqrt{x^2+1}+2017}{x+2018}=\dfrac{1}{2}\); \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+bx+1}-x\right)=2\). Tính P=4a+b
cho biết \(\lim\limits_{x\rightarrow-\infty}\dfrac{1-\sqrt{4x^2-x+5}}{a\left|x\right|+2}=\dfrac{2}{3}\). tính giá trị a?
tìm gioi han \(A=\lim\limits_{x\rightarrow-\infty}\dfrac{2ax+\sqrt{x^2+3x-1}}{3x+5}\)
tính giá trị \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-3x+6}+2x}{2x-3}\) ?
biết \(\lim\limits_{x\rightarrow+\infty}\left(\dfrac{x^2+1}{x-2}+ax-b\right)=-5\). tìm a, b?
