Please completely answer the following question with details. Do not only give partial answer.

3. In applications such as video games, is often computed to produce lighting and reflec- tion animations. Because each second in a video game requires millions and millions of computations of to produce the proper graphics, video games benefit from higher speed in using integer operations instead of floating point division to calculate va. The algorithm used to increase the speed to calculate was first implemented in the video game Quake III and in fact, calculates 4 times faster than using floating point division We will not explore this algorithm verbatim for numerous reasons. However, a critical part of this algorithm requires using Newton's Method to approximate the value of VE. Thus for this problem, you will use the Newton's Method to approximate v You are to do the following steps by hand and then write a code in Python implementing the algorithm to approximate Consider the equation f(y f(yn) Write out the Newton's Method for this equation, that is, write out: yn+1 yn- explicitly. You will have to find the derivative, f (y) by hand. Simplify your expression for yn+1 and covert any fractions to decimal form in your expression. Write a python script for the Newton's Method for this problem using the formula you found for y, +1 and the approximation to va. Use 0.3 for your initial guess and break from your code after a tolerance has been met. For your code, your input will be r where f(r)- Vi. Your code should print out the approximation ynti and the number of iterations it took to reach the tolerance