Solve the following problems, showing any necessary work. approximations (unless stated otherwise). l. Find the following limits algebraically. 3x 15 14 10 2x2 - 3x 3x2 -2 You must give EXACT answers, not decimal b. 2. iim 35 x'2 2x lim (sine 2 tan 0) (Hint: 011/4 Let f be the function defined by 3x2 -18 29 is a special angle.) if x < O if x = O if (0 < x) and (x < 2) if x = 2 if (2 < x) and (x < 3) if x = 3 3. 2x2 3x1 if 3 < x For each of a = O, a = 2, and a = 3, find lim f(x), lim f(x), and lim f(x), (writing DNE if that limit does not exist), and determine whether f(x) is continuous at x = a. Jse the Intermediate Value Theorem to show that there is a solution to the equation exsinxx = 2021 such that 7 S x S 8. (You do not need to solve this equation.)