Part $3$ Exercises

Recall that $a=$ last digit of your student ID$,b=$ second to last digit of your student ID$,c=$ third to last digit of your student ID$,$ and $d=$ the sum of the last three digits of your student ID$.$ Complete the following operations in your script, making new lines for each operation.

$3$A$)$ First, go to your Home menu in MATLAB, then click on Preferences. Next, click on Command Window, then in the Numeric format menu at the top, select long. This will ensure your approximations will output a large quantity of decimal places in the Command Window.

$3$B$)$ Determine a highly accurate estimate for $\sqrt[\phantom{2}]{m}$ by using Newton's method, where $m$ is the first prime number greater than $(d+1).$ Do so by solving $x^2-m=0$ by modifying the sample code written on the prior page, then use the two lines of code at the top of this page to check your results. Ensure your initial guess is a "nearby" whole number and choose $n5$ in the script.

$3$C$)$ Determine a highly accurate estimate for $\sqrt[\phantom{2}]{},$ and by extension, $,$ by using Newton's method. Do so by solving $x^4-2x^2+{}^2=0$ by modifying the sample code written on the prior page, then use the two lines of code at the top of this page to check your results. Ensure your initial guess is a "nearby" whole number and choose $n5$ in the script.

$3$D$)$ Determine an approximate solution to the equation $(a+1)x{e}^{-(b+1)x}-(c+1)x^2+(d+1)=0$ by using Newton's method. Modify the sample code written on the prior page, then use the two lines of code at the top of this page to check your results. Use an initial guess of $x_1=0$ and choose $n5$ in the script.

Once you have these operations written in proper MATLAB syntax, go to your Editor menu and click Run. If there are values in your Command Window for all operations without error messages, then your code has successfully compiled! If you have error messages, read them carefully and try to resolve them, then Run again.