Final Assignment for MT$471$S Please submit these programs by $16$:$00$ on $2022-12-16$ by: $-$ uploading the $,$ c files to the MT$471$S Moodle. You only need to submit the $.$ c file for each assignment. Your assignments are: $1.$ Write a program to calculate:

$\_0^$rsin $(\backslash$alpha x$)/$x d x

using the Simpson's rule. The program should read r and $\backslash$alpha from the user and then choose the number of steps by making sure that the step size, h$,$ satisfies h $<=0\mathrm{.}001/\backslash$alpha $.$ Hint $1$: You can get sin $($x$)$ using the function sin $($x$)$ from math. h$.$ Hint $2$: Be careful at x$=0!2.$ In question $1$ on assignment $3,$ we wrote a program that read a list of numbers and checked if each had a numbers had an inverse with respect to addition. In this question, you have to adapt your program to work with files. Write a program that reads the file numbers, txt which contains a list of numbers. It should make two new files: inverses.txt and noinverses $.$ txt$.$ The file called inverses.txt should contain all the numbers from the list that have an inverse. The file noinverses $-$ txt should contain all the other numbers. The program should also display how many numbers are in each file. For example, if numbers.txt contains $-2\mathrm{.}00\mathrm{.}03\mathrm{.}22\mathrm{.}0,$ then inverses. txt should contain $-2\mathrm{.}00\mathrm{.}02\mathrm{.}0$ and the noinverses.txt should contain $3\mathrm{.}2.$ The program would print a message to the screen saying: The numbers.txt file had $3$ numbers with inverses and $1$ number without. Hint $1$: Your program should use fopen, fscanf, fprintf and fclose. Hint $2$: As with the first program, you will probably want to use an array. You can assume that numbers. txt contains at most. $100$ numbers.