1.$\displaystyle

Suppose \mid f(x) \mid \leq \mid \frac{B}{x} \mid for\ all\ x\ not\ equal\ to\ 0.$

$\displaystyle Show\ that:

\lim_{x \to 0} ~ x^2f(x)=0

$

2.$\displaystyle

Suppose\ that\ \lim_{x \to 0} ~ f(x)=0\ and\ that\ \forall x \in R\ g(x) \leq B.$

$\displaystyle Show \lim_{x \to 0} ~ f(x)g(x)=0

$

Sorry, I don't even know where to start..