Ta có: \(\sqrt[n]{a}=a^{\dfrac{1}{n}}\)
\(\Rightarrow lim_{n\rightarrow\infty}\sqrt[n]{a}=lim_{n\rightarrow\infty}a^{\dfrac{1}{n}}=1\)
\(\Rightarrow lim_{n\rightarrow0^+}\sqrt[n]{a}=lim_{n\rightarrow0^+}a^{\dfrac{1}{n}}=+\infty\)
\(\Rightarrow lim_{n\rightarrow0^-}\sqrt[n]{a}=lim_{n\rightarrow0^-}a^{\dfrac{1}{n}}=0\)
tính \(A=lim\left[n\left(\sqrt{n^2+2}-\sqrt{n^2-1}\right)\right]\)
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\(\dfrac{\sqrt{n^2-4n}-\sqrt{4n^2+1}}{\sqrt{3n^2+1}-n}\)
a) \(lim\left(2n-\sqrt{9n^2+n}+\sqrt{n^2+2n}\right)\)
b)\(lim\sqrt{3^{n+1}+1}\)
c)\(lim\left(n+1+2^n\right)\)
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 \(\left(\sqrt{n^2+3n-1}-\sqrt[3]{n^3-n}\right)\)
Tính các giới hạn sau :
a) \(\lim\limits\left(n^2+2n-5\right)\)
b) \(\lim\limits\left(-n^3-3n^2-2\right)\)
c) \(\lim\limits\left[4^n+\left(-2\right)^n\right]\)
d) \(\lim\limits n\left(\sqrt{n^2-1}-\sqrt{n^2+2}\right)\)
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) \(\lim\limits\left(n^3+2n^2-n+1\right)\)
b) \(\lim\limits\left(-n^2+5n-2\right)\)
c) \(\lim\limits\left(\sqrt{n^2-n}-n\right)\)
d) \(\lim\limits\left(\sqrt{n^2-n}+n\right)\)
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 \(\lim\limits_{n->\infty}\left(\sqrt{an^2+bn+2}-2n\right)=2\)
Tìm các giới hạn sau:
\(a,lim\left(\sqrt{4n^2+5n}-2n\right)\)
\(b,lim\left(\sqrt{2n+1}-\sqrt{n}\right)\)
