To compute the central difference approximation for a function `f`

, we use the following formula:

We can write a script in MATLAB to calculate the central difference approximation for a vector of increasingly smaller values of `h`

as follows:

`main.m668 chars27 lines`

In this script, we define the function `central_diff`

to calculate the central difference approximation using the formula given above. We then define the function `f`

that we want to approximate the derivative of, as well as the point at which we want to compute the derivative `x0`

.

We define the vector `h_vec`

containing the values of `h`

that we want to use for the approximation, and initialize a vector `df_vec`

to store the results. We use a for loop to compute the approximation of `f'(2)`

for each value of `h`

, and store the results in `df_vec`

.

Finally, we plot the error in the approximation vs. `h`

using a logarithmic scale for both axes. We use the fact that `f'(2) = 2*cos(2) + 4`

to compute the exact value of the derivative at `x0`

, and plot the absolute value of the error. We can see from the plot that the error decreases as `h`

gets smaller, as expected.

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