Đặt \(S=\dfrac{1}{\sqrt{n^3+1}}+\dfrac{1}{\sqrt{n^3+2}}+...+\dfrac{1}{\sqrt{n^3+n}}\)
\(n^3+n>...>n^3+2>n^3+1\)
\(\Rightarrow\dfrac{n}{\sqrt{n^3+n}}< S< \dfrac{n}{\sqrt{n^3+1}}\)
Mà \(\lim\left(\dfrac{n}{\sqrt{n^3+1}}\right)=\lim\left(\dfrac{n}{\sqrt{n^3+n}}\right)=0\)
\(\Rightarrow\lim\left(S\right)=0\)
Tính các giới hạn sau
1,Lim\(\left(\dfrac{2n^3}{2n^2+3}+\dfrac{1-5n^2}{5n+1}\right)\)
2,a,Lim\(\left(\sqrt{n^2+n}-\sqrt{n^2+2}\right)\)
b,Lim\(\dfrac{\sqrt{n^4+3n-2}}{2n^2-n+3}\)
c,Lim\(\dfrac{\sqrt{n^2-4n}-\sqrt{4n^2+1}}{\sqrt{3n^2+1}-n}\)
Tìm các giới hạn sau:
a) \(lim\sqrt[3]{-n^3+2n^2-5}\)
b) \(lim\dfrac{1}{\sqrt{n+1}-\sqrt{n}}\)
c) \(lim\left(\dfrac{1}{n+1}-n\right)\)
d) \(lim\left(\dfrac{2n^2-1}{n+1}-2n\right)\)
e) \(lim\dfrac{2n^3+n^2-3n+1}{2-3n}\)
Tìm các giới hạn sau:
a)\(lim\left[n^2\left(\sqrt{n^2+2}-\sqrt{n^2+4}\right)\right]\)
b)lim( \(\dfrac{3}{n-2}-5n\))
c) lim(\(\dfrac{n-1}{\sqrt{3}-n}-\dfrac{4}{2^{-n}}\))
d) \(lim\left(\dfrac{n^2-4}{n-2}-\dfrac{3n^2+4}{n}\right)\)
e) \(lim\dfrac{\sqrt{n^2+1}-n\sqrt{5}}{\sqrt{n^2+1}+n\sqrt{5}}\)
Tìm các giới hạn sau:
\(a,lim\dfrac{\sqrt[3]{8n^3+2n}}{-n+3}\)
\(b,lim\dfrac{\left(2n\sqrt{n}+1\right)\left(\sqrt{n}+3\right)}{\left(n-1\right)\left(3-2n\right)}\)
tính các giới hạn sau:
a) lim (3n2+n2-1)
b)lim \(\dfrac{n^3+3n+1}{2n-n^3}\)
c) lim \(\dfrac{-2n^3+3n+1}{n-n^2}\)
d) lim \(\left(n+\sqrt{n^2-2n}\right)\)
e) lim \(\left(2n-3.2^n+1\right)\)
f) lim \(\left(\sqrt{4n^2-n}-2n\right)\)
g) lim \(\left(\sqrt{n^2+3n-1}-\sqrt[3]{n^3-n}\right)\)
tìm \(lim\dfrac{\left(2n\sqrt{n}+1\right)\left(\sqrt{n}+3\right)}{\left(n+1\right)\left(n+2\right)}\)
lim\(\dfrac{\left(2-n\right)\left(3+2n^3\right)}{2n^2-1}\)
lim\(\dfrac{\left(\sqrt{4n^2+1}-2n\right)n}{\sqrt[3]{4-n^3}+n}\)
Tính:
a) \(I=lim\dfrac{5^n+2^n}{3^n+4^n}\)
b) \(I=lim\dfrac{\sqrt{n^3+2n}+3n}{n+\sqrt{n^2+1}}\)
c) \(I=lim\left(\sqrt{2n^2+n}-\sqrt{n^2+2n+3}\right)\)
Tính :6/ lim\(\dfrac{-n^2+2n+1}{\sqrt{3n^4+2}}\)
7/ lim \(\dfrac{\sqrt{n^3-2n+5}}{3+5n}\)
10/ lim\(\dfrac{1+3+5+...+\left(2n+1\right)}{3n^3+4}\)
