To use central difference approximation to compute the first derivative of a function with increasingly smaller values of `h`

in MATLAB, we can define the following function:

`main.m295 chars11 lines`

We can then define the function we want to differentiate, e.g. `f = @(x) sin(x)`

, and loop over a range of decreasing values of `h`

while calling the `centraldiff`

function. Here's an example:

main.m252 chars10 lines

This will output:

main.m430 chars11 lines

As we can see, as `h`

gets smaller, the approximated derivative converges to the true value, which is 1 for `f(x) = sin(x)`

evaluated at `x=1`

.

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