1.
$\lim(u_n+1)=\lim u_n+\lim2=-3+2=-1$
2.
$\overrightarrow{u}.\overrightarrow{v}=|\overrightarrow{u}|.|\overrightarrow{v}|.\cos(\overrightarrow{u},\overrightarrow{v})=5.3.\cos60^o=\dfrac{15}{2}$
3.
$\lim\dfrac{4^n+5^n.5}{4^n+5^n}$
$=\lim\dfrac{\Big(\dfrac{4}{5}\Big)^n+5}{\Big(\dfrac{4}{5}\Big)^n+1}$
$=\dfrac{5}{1}=5$