Use first$-$order Taylor series expansion $($n$=1)$ to predict the function value of x $=3$ for the following equation. The initial point will be x $=1.$

a$)$ Calculate f$($x$)$ values between x $=1$ and x$=3$ with $0\mathrm{.}1$ increments using the equation above. These will be the true values.

Save the calculated true values $($f$($x$)$ values$)$ for all x values in one row vector called $"$y$\_$true".

b$)$ Use n$=1($first$-$order$)$ Taylor expansion to predict the function values for x values between x$=1$ and x$=3.$ Start the step size from h$=2.$ Decrease the step size by half $($i$.$e$.$ h$/2)$ until satisfying the following two conditions:

$($i$)$ the absolute true relative percent error between the true function value and predicted function value is below $5\%$ for x$=3.$ Assign the final true error as $"$et$\_$final"

$($ii$)$ The absolute approximate percent error between the current and previous function value is below $5\%$ for x$=3.$ Assign the final approximate error as $"$ea$\_$final"

Write MATLAB code for this using a "while" loop to continue until both the true and approximate relative percent error condition is below $5\%$ for x$=3.$ The while loop will stop when both the errors are below $5\%$ for x$=3.$ Save all taylor expansion predictions for each step size for all values between x$=1$ and x$=3.$