Write a Matlab function myLog that takes as input x and the number N and outputs as y the estimate of ln$($x$)$ using Eq$.(1)$ and the

corresponding true relative error tre. For the true value of ln$($x$)$ use Matlab$$s build$-$in function log$($x$)$ here and in the following

problems. Code the function such that it can handle both scalar and column vector inputs for x$,$ resulting in scalar, respective

column vector outputs for y and tre. If any of the values for x are x $<=1/2,$ i$.$e$.,$ Eq$.1$ is not applicable, call Matlab$$s error

function and output an appropriate error message. Do not print any results to screen or do any plotting within the function.

Required submission:

well commented script source code submitted to Canvas link $$Exam $1-$ Problem $2$;

Problem $3/$ MatlabGrader $(7$ points, CCOs #$1$ & #$11)$

Write a script to graph the result of Matlab$$s log$($x$)$ for $0\mathrm{.}500001<=$ x $<=10$ together with the results from myLog for N $=2,$

$8,$ and $16$ in a single figure. Use the transpose of Matlab$$s linspace command to generate a column vector x with $1001$ equally

spaced points covering the entire requested range of x values to generate the data for the plot.

Notes for the MatlabGrader script submission:

$$ Comment out clear or clear all in your script when submitting to MatlabGrader.

$$ Generate and store the figure handle examFig$1$ for the graph before doing any plotting commands, using

examFig$1=$ figure$(1)$;

$$ Properly label both axis using the appropriate variable names $($x$,$ ln$($x$)).$

$$ Include a legend for each line, starting with log$($x$)$ followed by N $=2,$ N $=8,$ and N $=16.$

$$ Ensure that your legend does not obstruct any part of your plot.

$$ Do not include the source code for myLog in your script. A correct version is used automatically on Matlab Grader.

Required submission:

$2$ well commented script source code submitted to Canvas link $$Exam $1-$ Problem $3$;

Problem $4/$ MatlabGrader $(5$ points, CCO #$1$& #$11)$

Write a script to graph the absolute of the true relative error of Eq$.(1)$ as a function of N at x $=5$ for N $=1,2,3,...200.$ Use a

logarithmic scale for the error and a linear scale for N $($Matlab$$s semilogy$()).$

Notes for the MatlabGrader script submission:

$$ Comment out clear or clear all in your script when submitting to MatlabGrader.

$$ Generate and store the figure handle examFig$2$ for the graph before doing any plotting commands, using

examFig$2=$ figure$(2)$