1. 1. Let f(x) = tan²(x). (a) Find the linearization of f at a = /3. (b) Use the result in part (a) to approximate tan²(1) to three decimal places. 2. Findthe exact values of the absolute extrema of each of the following. (a) f(x) = x root(5-x on [1, 5] (b) f(x) = sin x (3) cos x on [0, 2] 3. Using the Intermediate Value Theorem and Rolle's Theorem, show that the equation 1/2x sin x = 0 has exactly one real root on(/2, ).