Question

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= \(lim\dfrac{3^n+5.4^n}{4^n+2^n}\)

Answer 1

\(a=\lim\dfrac{\dfrac{1}{n}+\dfrac{1}{n^2}}{1+\dfrac{2}{n}}=\dfrac{0}{1}=0\)

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

\(c=\lim\dfrac{\sqrt{9-\dfrac{1}{n}-\dfrac{1}{n^2}}}{4-\dfrac{2}{n}}=\dfrac{\sqrt{9}}{4}=\dfrac{3}{4}\)

\(d=\lim\dfrac{\left(\dfrac{3}{4}\right)^n+5}{1+\left(\dfrac{2}{4}\right)^n}=\dfrac{5}{1}=5\)