\(=lim\sqrt{\frac{n\left(n+1\right)^2}{2n^4+n^2+1}}=lim\sqrt{\frac{n^3+2n^2+n}{2n^4+n^2+1}}=lim\sqrt{\frac{\frac{1}{n}+\frac{2}{n^2}+\frac{1}{n^3}}{2+\frac{1}{n^2}+\frac{1}{n^4}}}=\frac{0}{2}=0\)
Chương 4: GIỚI HẠN
Các câu hỏi tương tự
lim \(\frac{\left(2n^2-3n+5\right)\left(2n+1\right)}{\left(4-3n\right)\left(2n^2+n+1\right)}\)
lim \(\frac{\sqrt{n^4+1}}{n}-\frac{\sqrt{4n^6+2}}{n^2}\)
lim \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
a)lim \(\frac{\left(2n+1\right)^2\left(n-1\right)}{\sqrt[3]{n^3+7n-2}}\)
b)lim [(2n-1)\(\sqrt{\frac{2n^2+5}{n^4+n^2+2}}\)]
c)lim [n(\(\sqrt[3]{n^3+n^2}-n\))]
a; lim\(\frac{\sqrt{6n^4+n+1}}{2n^2+1}\)
b; lim \(\frac{\left(n+1\right)\left(2n+1\right)^2\left(3n+1\right)^3}{n^2\left(n+2\right)^2\left(1-3n\right)^2}\)
1 a,Limsqrt{1+2n-n^3}b,Limsqrt{n^2+2n+3}-sqrt[3]{n^2+n^3}c,Limdfrac{left(2sqrt{n}+1right)left(sqrt{n}+3right)}{left(n+1right)left(n+2right)}d,dfrac{4^{n+1}-3times2^n}{3^{n+2}+2^n}e,dfrac{7^{n+1}-5^{n+2}+3}{2times6^{n+1}-3^n+3}f,dfrac{sqrt{n^4+1}}{n} -dfrac{sqrt{4n^6+1}}{n}
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1
a,Lim\(\sqrt{1+2n-n^3}\)
b,Lim\(\sqrt{n^2+2n+3}-\sqrt[3]{n^2+n^3}\)
c,Lim\(\dfrac{\left(2\sqrt{n}+1\right)\left(\sqrt{n}+3\right)}{\left(n+1\right)\left(n+2\right)}\)
d,\(\dfrac{4^{n+1}-3\times2^n}{3^{n+2}+2^n}\)
e,\(\dfrac{7^{n+1}-5^{n+2}+3}{2\times6^{n+1}-3^n+3}\)
f,\(\dfrac{\sqrt{n^4+1}}{n}\) -\(\dfrac{\sqrt{4n^6+1}}{n}\)
tính giới hạn
1.\(\lim\limits\left(n^3+4n^2-1\right)\)
2.\(lim\dfrac{\left(n+1\right)\sqrt{n^2-n+1}}{3n^2+n}\)
3.\(lim\dfrac{1+2+....+n}{2n^2}\)
4.\(lim\dfrac{3^n-4.2^{n-1}-10}{7.2^n+4^n}\)
tính các giới hạn sau:
a, lim\(\frac{n^{2020}-n+1}{n^{2022}+2n-3}\)
b, lim(\(\sqrt[3]{n^3-2n^2}-n\))
c, lim \(\left(\sqrt{n^2+3n}-n+2\right)\)
d, lim \(n\left(\sqrt{n^2-1}-\sqrt{n^2+2}\right)\)
tínha.limlimits_{n-+infty}dfrac{n^5+n^2-n+2}{left(2n^3-1right)left(n^2+n+1right)}b.limlimits_{n-+infty}dfrac{sqrt{n^2-n+2}}{n+2}c.limlimits_{n-+infty}dfrac{n-sqrt[3]{n^2-n^3}}{n^2+n+1}d.limlimits_{n-+infty}left(n-sqrt{n^2+n+1}right)
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tính
a.\(\lim\limits_{n->+\infty}\dfrac{n^5+n^2-n+2}{\left(2n^3-1\right)\left(n^2+n+1\right)}\)
b.\(\lim\limits_{n->+\infty}\dfrac{\sqrt{n^2-n+2}}{n+2}\)
c.\(\lim\limits_{n->+\infty}\dfrac{n-\sqrt[3]{n^2-n^3}}{n^2+n+1}\)
d.\(\lim\limits_{n->+\infty}\left(n-\sqrt{n^2+n+1}\right)\)
lim \(\frac{\left(2n^2+1\right)^4\left(n+1\right)^9}{n^{17}+1}\)
Tìm giới hạn các dãy số saua) limdfrac{2^n+6^n-4^{n-1}}{3^n+6^{n+1}}b) limdfrac{1+3+5+...+left(2n+1right)}{3n^2+4}c) limdfrac{1+2+3+...+n}{n^2-3}d) limleft[dfrac{1}{1.2}+dfrac{1}{2.3}+...+dfrac{1}{nleft(n+1right)}right]e) limleft[dfrac{1}{1.3}+dfrac{1}{3.5}+...+dfrac{1}{left(2n-1right)left(2n+1right)}right]
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Tìm giới hạn các dãy số sau
a) \(lim\dfrac{2^n+6^n-4^{n-1}}{3^n+6^{n+1}}\)
b) \(lim\dfrac{1+3+5+...+\left(2n+1\right)}{3n^2+4}\)
c) \(lim\dfrac{1+2+3+...+n}{n^2-3}\)
d) \(lim\left[\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{n\left(n+1\right)}\right]\)
e) \(lim\left[\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\right]\)