$ta{n}^{-1}x=x-\frac{x^3}{3}+\frac{x^5}{5}-$cdots$={\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n\frac{x^{2n+1}}{2n+1}$

a$)$ Write a user$-$defined function that determines $ta{n}^{-1}x$ using the above Taylor series. For function name and arguments use $y=$atanTaylor$(x),$ where the input argument is $x$ and the output argument $y$ is the approximate value for $ta{n}^{-1}x$ obtained using Taylor's series expansion. Inside the user$-$defined function, create a loop for adding the terms of the series.

b$)$ Use your function atanTaylor to calculate $ta{n}^{-1}0\mathrm{.}5$ and $ta{n}^{-1}0\mathrm{.}9$ and report the outputs. Include your atanTaylor function and the commands that call your function in your submission along with the outputs of your code.

c$)$ Compare the values calculated in part $($b$)$ using atanTaylor with the values obtained by using MATLAB's built$-$in function atan.

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