Let f(x) = 3x+x -2. a. Find an interval where the function f has one root. b. Use Rolle's theorem to show that the function f has exactly one root. (4 points) 10. Use the identity cosx+ sinx = 1 to integrate [cosx sinx dx. (12 points) 11. Evaluate each of the definite integrals listed below 7/6 cos (3x) dx b. sin(2x) sin x dx + cos(2x) dx a. C. 0 (6 points) 12. Apply the fundamental theorem of calculus to find the following derivative tan(31) dt. d dx -x