$\lim U_{n} =\lim \sqrt{4n-1}-\sqrt{n+2}=\lim \sqrt n . \left ( \sqrt{4-\dfrac{1}{\sqrt n}}-\sqrt{1+\dfrac{2}{\sqrt n}} \right ) =+\infty.(2-\sqrt 2)=+\infty.$
$\lim U_{n} =\lim \sqrt{4n-1}-\sqrt{n+2}=\lim \sqrt n . \left ( \sqrt{4-\dfrac{1}{\sqrt n}}-\sqrt{1+\dfrac{1}{\sqrt n}} \right ) =+\infty.(2-1)=+\infty.$
$\lim U_{n} =\lim \sqrt{4n-1}-\sqrt{n+2}=\lim \sqrt n . \left ( \sqrt{4-\dfrac{1}{\sqrt n}}-\sqrt{1+\dfrac{
2}{\sqrt n}} \right ) =+\infty.(2-
\sqrt 2)=+\infty.$