Question

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) \(lim\dfrac{\sqrt{3n^2+2n}-n}{3n-2}\)

Answer 1

\(a=\lim\dfrac{5n\left(n+\sqrt{n^2-n-1}\right)}{n+1}=\lim\dfrac{5\left(n+\sqrt{n^2-n-1}\right)}{1+\dfrac{1}{n}}=\dfrac{+\infty}{1}=+\infty\)

\(b=\lim\dfrac{\sqrt{\dfrac{1}{n}+\sqrt{\dfrac{1}{n^3}+\dfrac{1}{n^4}}}}{1-\dfrac{1}{\sqrt{n}}}=\dfrac{0}{1}=0\)

\(c=\lim\dfrac{\sqrt{2n^2-1+\dfrac{7}{n^2}}}{3+\dfrac{5}{n}}=\dfrac{+\infty}{3}=+\infty\)

\(d=\lim\dfrac{\sqrt{3+\dfrac{2}{n}}-1}{3-\dfrac{2}{n}}=\dfrac{\sqrt{3}-1}{3}\)