e,
$\lim\dfrac{5^n+4.10^n}{2.10^n+3^n}$
$=\dfrac{\dfrac{1}{2^n}+4}{2+\Big(\dfrac{3}{10}\Big)^n}$
$=\dfrac{4}{2}=2$
f,
$\lim\dfrac{\sqrt{n^2-3n}}{n+1}$
$=\lim\dfrac{n\sqrt{1-\dfrac{3}{n}}}{n+1}$
$=\lim\dfrac{\sqrt{1-\dfrac{3}{n}}}{1+\dfrac{1}{n}}$
$=1$