I have never felt so lost in my life, so far.

Hopefully someone can help.

The section is on "The Precise Definition Of A Limit"

Suppose that $\displaystyle \lim\ _{x \to a}\ f(x)=\infty$ and $\displaystyle \lim\ _{x \to a}\ g(x)= c$, where $\displaystyle c$ is a real number. Prove each statement.

$\displaystyle (a)$ $\displaystyle \lim_{x \to a}[f(x)+g(x)]=\infty$

$\displaystyle (b)$ $\displaystyle \lim_{x \to a}[f(x)g(x)]=c$ if $\displaystyle c>0$

$\displaystyle (b)$ $\displaystyle \lim_{x \to a}[f(x)g(x)]=-\infty$ if $\displaystyle c<0$

Am I supposed to use the triangle inequality? I think that if someone can help with problem (a), then I should be able to figure out the rest. Thanks!