Problem A. 1 Determine A, B1 C such that all of the following functions intersect the point [2, 2]: f1($)=A:r+1 fszl=BI2+2 f3[:z:]=C:c3+3 Problem A. 2 Find all :1: E R that are solutions to this equation: 0 = {1 :1: :32 ...) ~ (2 1r a" Problem A.3 Find the derivative f'(:r} of the following function with respect to :c: fit-T) : Sir]. (sinn: + Trans :1!) Problem B.1 Let H define the sum of reciprocals of all integers from 1 to n: Hn = 1+ 09 K + +...+ n Prove the following identity: 1 Han - Hn =1 - I ... + 2n - 1 2nProblem B.2 It is well known that squared brackets do not simplyr square the individual terms: {1 +3972 19+? (1+2+3)'~'72 12+22+32 Instead, we add a correction term 1;!) to make the equations hold true: [1 +2}2 = 12+22 +2 [1+2+3)"'=1"'+2"'+32'+1;3;3 [1+2+3+ +n}2 = 12+22+32+... +n2+wn Show that the correction term uh\" has the following form and determine the values of or and ,8: 4 2 3 '31 '?'I|.'. \"H, 'Il 11511.: a + '6 Problem B.3 You are given two overlaying squares with side length a. One of the squares is xed at the bottom right corner and rotated by an angle of o: (see drawing}. Find an expression for the enclosed area A{o] between the two squares with respect to the rotation angle 0:. Problem C.1 For this problem, we define the fractional part of r E R> as {x} = x- [x] where [xx ] is the integer part of x, i.e., the greatest integer less than or equal to r. (a) Draw the function {x} in a coordinate system for 0