Lời giải:
\(\lim\limits\frac{\sqrt{n\sqrt{2n\sqrt{4n}}}}{n+1}=\lim\limits\frac{\sqrt{2n^{\frac{7}{4}}}}{n+1}=\lim\limits\frac{\sqrt{\frac{2}{n^{\frac{1}{4}}}}}{1+\frac{1}{n}}=0\)
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\(\dfrac{\sqrt{n^2-4n}-\sqrt{4n^2+1}}{\sqrt{3n^2+1}-n}\)
Tính các giới hạn sau:
\(lim\sqrt{n}\left(\sqrt{n+1}-n\right)\)
\(lim\dfrac{\sqrt{4n^2+1}+2n-1}{\sqrt{n^2+4n+1}+n}\)
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 các giới hạn sau:
a) \(lim\dfrac{5n}{n-\sqrt{n^2-n-1}}\)
b) \(lim\dfrac{\sqrt{n+\sqrt{n+1}}}{n-\sqrt{n}}\)
c) \(lim\dfrac{\sqrt{2n^4-n^2+7}}{3n+5}\)
d) \(lim\dfrac{\sqrt{3n^2+2n}-n}{3n-2}\)
Tìm các giới hạn sau:
a) \(lim\left(\sqrt{4n+1}-2\sqrt{n}\right)\)
b) \(lim\left(\sqrt{n^2+2n}-\sqrt{n^2-2n}-n\right)\)
c) \(lim\left(\sqrt{9^n-3^n}-4^n\right)\)
d) \(lim\left(3n^3+2n^2+n\right)\)
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) \(lim\dfrac{2n^3+n^2-3n+1}{2-3n}\)
có bao nhiêu giá trị nguyên a để \(lim\dfrac{\sqrt{an^3+n^2+1}-n\sqrt{2n+1}}{\sqrt{4n^3+3n}}\le\sqrt{2}\)
lim\(\dfrac{\left(2-n\right)\left(3+2n^3\right)}{2n^2-1}\)
lim\(\dfrac{\left(\sqrt{4n^2+1}-2n\right)n}{\sqrt[3]{4-n^3}+n}\)
Tìm các giới hạn sau:
\(a,lim\left(\sqrt{4n^2+5n}-2n\right)\)
\(b,lim\left(\sqrt{2n+1}-\sqrt{n}\right)\)
