Suppose that f and g are real functions such that $\displaystyle f(x),g(x)\to\infty\$, as $\displaystyle x\to\infty\$.

Prove that $\displaystyle f(x)+g(x)\to\infty\$ as $\displaystyle x\to\infty\$ approaches infinity.

What (if anything) can be said in general about the difference $\displaystyle f(x)-g(x)$, the product $\displaystyle f(x)g(x)$ and the quotient $\displaystyle \frac{f(x)}{g(x)}$ as $\displaystyle x\to\infty\$??

Justify any assertions that you make.