Problem 5. Write a dynamic programming based version of the factorial function and prove its time complexity.

Write a MatLab user-defined function that determines the coefficients of a cubic polynomial, f(x)=a₂x³ + a₂x² + a₁x + a that best fits a given set of data points. The function should also calculate the overall error E. Name the function [a,Er] = CubPolFit(x,y), where the input arguments x and y are vectors with the coordinates of the data points, and the output argument a is a four-element vector with the values of the coefficients a3, a₂, a₁, a. The output argument Er is the value of the overall error. " (a) Use CubPolFit to find the cubic polynomial that best fits the data in the rubber tension tests (see lecture slides): Curve fitting - polynomial regression - Example A tension test is conducted for determining the stress-strain be- havior of rubber. The data points from the test are shown in the figure, and their values are given below. Determine the fourth order polynomial that best fits the data points. Make a plot of the data points and the curve that corresponds to the…

For the first problem, in parts b and c, how are the variables being taken from functions that they are not defined in? To clarify, in part c, how is the variable "b" taken from fun2 when it is not defined in that in function. Shouldn't the answer there just be "b(fun1)"

Determine if each function is injective, surjective or bijective. Give one counterexample for each that it is not. 1. function f from {a,b,c,d} to itself, where f(a) = d,  f(b) = b,  f(c) = a,  f(d) = c