## Problem 1: Given the following data for the results of Test 1 for course MATH2100 (a) Create the histogram for the number of observation and relative frequency for the above data. (b) Create the cumulative frequency. (c) Find the mode, mean, median and standard deviation for the above. (d) Use Microsoft Excel and MatLab and check your results.

EXPERT ANSWER First of all insert the values in MSExcel and add one relative frequency column, and insert a graph (histogram)

## Let f(x) = e* -2- x, and starting with (-2.4,-1.6]. Write one C++ program that does the following: a. C. Find the roots of f(x) = 0 accurate to 3 x 10′ using the Bisection Method. b. Print all approximated roots Cn. Print the number of iterations needed to reach given accuracy using Bisection Method. d. Find the roots of f(x) = 0 accurate to 4.5 x 10 using the False Position Method. e. Print all intervals (a, b). f. Print the number of iterations needed to reach given accuracy using False Position Method. Note: given accuracy is 8 Active Wind

EXPERT ANSWER C++ code:- #include <iostream> #include <cmath> using namespace std; #define EP 0.01 // An example function whose solution is determined using // Bisection Method. The function is exp(x)-2-x double solution(double x) { return exp(x)- 2-x; } // Prints root of solution(x) with error in EPSILON void bisection(double a, double b) { if (solution(a) …

## In Example 4.29 we deduced the equipotence [0, 1] ≈ (0, 1) by invoking the Schr¨oder–Bernstein theorem, but we didn’t actually construct a bijection [0, 1] → (0, 1). (a) Verify that the function h given by the following scheme is such a bijection:

How do you prove surjection for the middle function? EXPERT ANSWER Answer :- Bijective. Alternatively, f is bijective if it is a one-to-one correspondence between those sets, in other words both injective and surjective. Example: The function f(x) = x2 from the set of positive real numbers to positive real numbers is both injective and surjective. Thus it is also bijective.