lim\(\frac{3n^2+n-5}{2n^2+1}\)=lim\(\frac{n^2\left(3+\frac{1}{n}-\frac{5}{n^2}\right)}{n^2\left(2+\frac{1}{n}\right)}\)=\(\frac{3}{2}\)
lim\(\frac{\sqrt{9n^2-n}+1}{4n-2}\)=lim\(\frac{n\sqrt{9-\frac{1}{n}+\frac{1}{n^2}}}{n\left(4-\frac{2}{n}\right)}\)=lim\(\frac{\sqrt{9}}{4}\)=\(\frac{3}{2}\)
\(lim\left(\sqrt[3]{n-n^3}+\sqrt{n^2+3n}\right)\)
\(lim\left(\sqrt{n-2\sqrt{n}}-\sqrt{n+4}\right)\)
\(lim\left(\sqrt[3]{3n^2+n^3}-n\right)\)
\(lim\left(\sqrt[3]{n^3+6n}-\sqrt{n^2-4n}\right)\)
\(lim\frac{-3^{n+1}+4^{n+1}}{5.3^n+3.2^{2n-1}}\)
\(lim\left(\frac{3^{2n}-5^{n+1}+7^{n+1}}{3^{n+2}+5^n+2^{3n+2}}\right)\)
\(lim\left(\frac{6^{n+1}+3^{2n+5}}{3^{2n+3}-2^{2n-1}}\right)\)
tìm các giới hạn
a)lim(\(\sqrt{n+1}-\sqrt{n}\))
b)lim\(\left(\sqrt{n+5n+1}-\sqrt{n^2-n}\right)\)
c)lim\(\left(\sqrt{3n^2+2n-1}-\sqrt{3n^2-4n+8}\right)\)
d)lim\(\frac{2^n+6^n-4^{n+1}}{3^n+6^{n+1}}\)
e)lim\(\frac{3^n-4^n+5^n}{3^n+4^n-5^n}\)
f)lim\(\frac{1+3+5+.....+\left(2n+1\right)}{3n^2+4}\)
g)lim[\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{n\left(n+1\right)}\)]
h)lim\(\frac{1^2+2^2+3^2+.....+n^2}{n\left(n+1\right)\left(n+2\right)}\)
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\(\dfrac{\sqrt{n^2-4n}-\sqrt{4n^2+1}}{\sqrt{3n^2+1}-n}\)
Tìm các giới hạn sau:
a) \(lim\left(4^n-3^n\right)\)
b) \(lim\left[\left(2^n+1\right)^2-4^n\right]\)
c) \(lim\left(\sqrt{2n^5-3n^2+11}-n^3\right)\)
d) \(lim\left(\sqrt{2n^2+1}-\sqrt{3n^2-1}\right)\)
e) \(lim\sqrt{n^2+3n\sqrt{n}+1}-n\)
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) \(lim\left(\sqrt{4n+1}-2\sqrt{n}\right)\)
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) \(lim\left(3n^3+2n^2+n\right)\)
5/ lim \(\frac{\left(12-n\right)^3\left(n-2\right)}{\sqrt{n^8-1}-2n^4}\)
6/ lim \(\frac{\sqrt[3]{3-8n^3}-n}{2n+5}\)
7/ lim \(\frac{\sqrt{n^6-2n+1}}{\sqrt{4n^6+3n}}\)
8/ lim \(\left(n^4+2n-20\right)\)
Tính:
A= \(lim\dfrac{n+1}{n^2+2n}\)
B= \(lim\left(-2n^3+n^2+2\right)\)
C= \(lim\dfrac{\sqrt{9n^2-n-1}}{4n-2}\)
D= \(lim\dfrac{3^n+5.4^n}{4^n+2^n}\)
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) \(lim\dfrac{\sqrt{3n^2+2n}-n}{3n-2}\)
