Use Matlab to compute the approximation of the derivative of tan x at

x

= 1

.

0, with the

formula in (4), with smaller and smaller values of h

. Plot the error e as a function of h, use log

scale (see Matlab command loglog). How did you expect the error to behave? How does the actual error behave? For what h value do you get the best result? What do you think is the cause of this behavior?

Let the function f(x) be three times differentiable. Consider the finite difference approximation formula Note that this scheine uses values of f at the three points z, z + h,z + 2h. This is a one-sided finite difference (d . Use Matlab to compute the approximation of the derivative of tanz at 1.0, with the formula in (4), with smaller and smaller values of h. Plot the error e as a function of h, use log scale (see Matlab command loglog). How did you expect the error to behave? How does the actual error behave? For what h value do you get the best result?What do you think is the causc of this behavior? What to hand in for part (d): Hand in the Matlab script file, the relevant output of your code, the plots of errors, and your comments