In Calculus, the derivative of a function $f(x)$ is given by $f'(x)$ which is
$$f'(x)=\frac{f(x+h)-f(x)}{h},$$
in the limit as $h\rightarrow 0$. Let's test this defintion here. Think of a function
$f(x)$ and it's derivative, $g(x)$. As example, if $f(x)=sin(x)$ then $g(x)=cos(x)$.
Let's compute $f'(x)$ according to the definition above, letting $h$ get smaller and smaller,
and compare $f'(x)$ at some $x$ with the analytical derivative, $g(x)$ at the same $x$. Let's
see what we get.

`return`

statements in both the f(x) and g(x) functions. Then fix the maximum value of `i`

you wish
to run through in the for-loop.
Type your code here:

See your results here:

This code will not run! You have to put in a function in the

`return`

statement in the `function f(x)`

defintion,
and its derivative in the `return`

statement in the `function g(x)`

definition. Lastly, how many runs via the `for`

loop do you want to run? This is a big question. How many interations of this do you want to run until you are convinced
that the definition of the derivative (above) is valid? (Note: to make $h\rightarrow 0$ as needed, we cut it by $1/4$ each
time through the loop. This is the best a computer will get at taking a limit.)