Question

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) \(lim\left(3n^3+2n^2+n\right)\)

Answer 1

\(a=\lim\dfrac{1}{\sqrt{4n+1}+2\sqrt{n}}=\dfrac{1}{\infty}=0\)

\(b=\lim n\left(\sqrt{1+\dfrac{2}{n}}-\sqrt{1-\dfrac{2}{n}}-1\right)=+\infty.\left(-1\right)=-\infty\)

\(c=\lim4^n\left(\sqrt{\left(\dfrac{9}{16}\right)^n-\left(\dfrac{3}{16}\right)^n}-1\right)=+\infty.\left(-1\right)=-\infty\)

\(d=\lim n^3\left(3+\dfrac{2}{n}+\dfrac{1}{n^2}\right)=+\infty.3=+\infty\)