Question

Giúp mình câu 18,19,20 với ạ

Answer 1

18.

Hiển nhiên A là mệnh đề sai, ví dụ: \(u_n=n^2\) và \(v_n=n\)

19.

\(-1\le cos2n\le1\Rightarrow\dfrac{-1}{n^2+1}\le\dfrac{cos2n}{n^2+1}\le\dfrac{1}{n^2+1}\) với mọi n

Mà \(\lim\left(-\dfrac{1}{n^2+1}\right)=\lim\left(\dfrac{1}{n^2+1}\right)=0\)

\(\Rightarrow\lim\dfrac{cos2n}{n^2+1}=0\Rightarrow\lim\left(5-\dfrac{cos2n}{n^2+1}\right)=5-0=5\)

20.

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

\(\lim\left(\dfrac{2}{n}-1\right)=-1< 0\)

\(\lim\left(\dfrac{1}{\sqrt{n}}\right)=0\) và \(\dfrac{1}{\sqrt{n}}>0\)

\(\Rightarrow\lim\left(\dfrac{2-n}{\sqrt{n}}\right)=-\infty\)