UDF and anonymous function question. Use long format to do this question. You must create two $.$m files: one is a UDF function file for step b$,$ and one is a script file that includes all steps from a to e$.$

Taylor series expansion is an infinite sum of terms that are expressed in terms of the function$$s derivatives at a single point. The series is often used to simply approximate a function around a point.

In this question, we are going to estimate the errors between the original function and approximate function $($Taylor series$)$

You are given an original function $(1-$x$)$ and its Taylor series:

$(1-$x$)=1-$x$/2-$x$^2/8-$x$^3/16-(5$x$^4)/128+$O$($x$^5)$

a $-$ Use Matlab command to create a vector x range from $-0\mathrm{.}5$ to $0\mathrm{.}5$ with step size of $0\mathrm{.}05.$

b $-$ Create a user$-$defined function $($UDF$)$ for the defined function y$($x$)$ that has one input x and one output y$.$ You may name the UDF q$1$UDF. Call this function with the input x vector created in a$,$ name the output vector as y$\_$UDF. Copy and paste the UDF code.

y$($x$)=1-$x$/2-$x$^2/8-$x$^3/16-(5$x$^4)/128$

c $-$ Create an anonymous function for the above defined function y$($x$)$ that has one input x and one output y$.$ You may name the anonymous function q$1$AF$.$ Call this function with the input x vector created in a$,$ name the output vector as y$\_$anonymous. Copy and paste the script.

d $-$ Use Matlab command $$sqrt$(1-$x$)$ to get a new vector with the input x vector created in a$,$ name the output vector as y$\_$matlab.

e $-$ To compare the difference of two vectors A & B$,$ we can use Matlab command $$norm$$ to compute norm of $($A$-$B$).$ Compute the following two errors to compare our function calculations:

error$1=$ norm$($y$\_$anonymous $$ y$\_$UDF$)$

error$2=$ norm$($y$\_$matlab $$ y$\_$UDF$)$