$\displaystyle f_{n},g_{n}$ are sequences of functions :$\displaystyle X\rightarrow R$ which converge uniformly to f,g respectively.

If $\displaystyle \lambda\in R $, prove $\displaystyle \lambda f_{n}$ converges uniformly to $\displaystyle \lambda f $

and

prove : $\displaystyle f_{n}g_{n} $ converges to $\displaystyle fg $ given f,g are bounded.