Problem A. 1 Determine A, B1 C such that all of the following functions intersect the point [2, 2}: 191(3) =AIF+1 3H1?) =BI2+2 f3{:1:] 2033313 Problem A.2 Find all x E R that are solutions to this equation: 0 = (1 -x - x2 -...) . (2-x - 22 - ...)Problem A.3 Find the derivative f'{:t:] of the following function with respect to 11:: f(33) = sin (175m: + 'JTCUG \") Problem B. 1 Let H\" dene the sum of reciprocals of all integers from 1 to n: H 1+1 1 1 n +2 3+4+m+n Prove the following identity: Problem B.2 It is well known that squared brackets do not simply square the individual terms: {1 +2)? 7E 1H22 (1+2+3)27v12+2'3+32 Instead, we add a correction term 1,!) to make the equations hold true: [1 +2)2 = 13+? +1.92 [1+2+3)9=12+22+32+1b3 (1+2+3+...+n)9=12+22+32+...+n2+wn Show that the correction term if)\" has the following form and determine the values of Cr and f3: Problem B.3 You are given two overlaying squares with side length a. One of the squares is fixed 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 a. A AProblem C.1 For this problem, we define the fractional part of r E Ryo as {x} = x- [x] where [x] is the integer part of x, i.e., the greatest integer less than or equal to x. (a) Draw the function {x} in a coordinate system for 0