\(=lim\left[n\left(\sqrt{4+\frac{1}{n^2}}-2+2-\sqrt[3]{8+\frac{1}{n^2}}\right)\right]\)
\(=lim\left[n\left(\frac{\frac{1}{n^2}}{\sqrt{4+\frac{1}{n^2}}+2}-\frac{\frac{1}{n^2}}{4+2\sqrt[3]{8+\frac{1}{n^2}}+\sqrt[3]{\left(8+\frac{1}{n^2}\right)^2}}\right)\right]\)
\(=lim\left(\frac{\frac{1}{n}}{\sqrt{4+\frac{1}{n^2}}+2}-\frac{\frac{1}{n}}{4+2\sqrt[3]{8+\frac{1}{n^2}}+\sqrt[3]{\left(8+\frac{1}{n^2}\right)^2}}\right)=\frac{0}{2+2}-\frac{0}{4+4+2}=0\)
\(1.lim\left(\sqrt[3]{8n^3+4n^2+1}-\sqrt[3]{8n^3-2}\right)\)
\(2.lim\left(\sqrt[3]{n^3+n^2+1}+\sqrt[3]{8-n^3}\right)\)
\(3.lim\left(\sqrt[3]{n^3+n^2+2}-n\right)\)
Tính: Lim\(\left(\sqrt{n^2+2}.\sqrt[3]{8n^3+1}-\sqrt{4n^2+1}.\sqrt[3]{n^3+2}\right)\)
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 \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
\(lim\left(\sqrt{4n^2+2n+1}-\sqrt[3]{8n^3-3n^2+1}\right)\)
Tìm giới hạn lim un
a. \(u_n=\left(2-3n\right)^4\left(n+1\right)^3\)
b.\(u_n=\sqrt[3]{n+4}-\sqrt[3]{n+1}\)
c.\(u_n=\sqrt[3]{8n^3+3n^2+4}-2n+6\)
d. \(\sqrt[3]{8n^3+3n^2-2}+\sqrt[3]{5n^2-8n^3}\)
Help me ! Gợi ý cho mik cx đc ạ . Tks mng
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.\(lim\dfrac{3^n-4.2^{n-1}-10}{7.2^n+4^n}\)
lim n(\(\sqrt[3]{n^3-3n^2}-3n\))
lim (\(\sqrt{4n^2+n}+\sqrt[3]{2n^2-8n^3}\))
Tìm giới hạn sau \(lim\dfrac{\left(3n+1\right)\left(1-8n\right)}{\sqrt[3]{n^3+3n-9}}\)
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,\(\dfrac{\sqrt{n^4+1}}{n}\) -\(\dfrac{\sqrt{4n^6+1}}{n}\)