Plot the function $y=x+sin(x)$ over the interval $0x{x}_{\text{m}\text{a}\text{x}},$ using a while loop to determine the value of $x_{\text{m}\text{a}\text{x}}$ with $2$ decimal places, such that $y(x_{\text{m}\text{a}\text{x}})=5\mathrm{.}7.$ Notice that you cannot determine the value of max ${?}^2$ explicitly.

Create a program using the for$-$end loop to calculate the first $20$ terms of the equation $($use an input command to enter $($:$x^{\text{'}}\})$:

$e^x={\displaystyle \underset{n=0}{\overset{x}{}}}\frac{1}{n!}{x}^n$

Test the program for several values of $x($for example, $1,25,6).$