Two functions f(x) and g(x), when divided, do not produce a constant ratio. However, for very large values of x, the ratio is almost 0. Find an example of f(x) and g(x) to illustrate this phenomenon. Repeat this procedure to produce a ratio almost equal to 2 for large values of x.

Extension
Find two functions f(x) and g(x) that produce a ratio of n when examining large values of x.