Question

Express the relationship f (x) is o(g(x)) using a picture. Show the graphs of f (x), g(x), and f (x)/g(x).

Short answer

This is based on the concept of little o notation.

Step-by-step solution

Step 1: 

Let us plot f(x) ,g(x) and$\frac{f\left(x\right)}{g\left(x\right)}$ on a graph.

We see that$\frac{f\left(x\right)}{g\left(x\right)}$ approaches to 0 when $x\ge 1$. Now to prove this we now use our little o notation.

Step 2:

By the definition of little o notation,

$\underset{x\to \mathrm{\infty }}{lim} \frac{f\left(x\right)}{g\left(x\right)}=0$

Which is true if we look at the graphs,