9. lim f(x) x-1 (a) is 0 (b) is 1/2 (c) is 2cos2 (d) does not exist Solution. From the solution above, a - 1 f (ac ) = cos(2(x - 1) = tan (2x - 2) 2 sin (2(x -1) 2(x - 1) sin 2(x - 1) Using lim = 1, and lim cos 2(x - 1) = 1, so the limit is 1/2 x-1 2(2 - 1) x-1 and the answer is (b)