Total: 45 marks NOTE: SHOW ALL YOUR WORK FOR THE PROBLEM ON THIS PAGE. UNJUSTIFIESD ANSWERS MAY RECEIVE LITTLE OR NO CREDIT. (1) (4 marks) Find the domain of the function f(x) = In(cos-1(x + 2)). (2) (4 marks) Find an exponential function f (x) = bf + a that passes through the points (1, 4) and (2, 10) . (3) (9 marks) Evaluate (a) tan 1 ( tan (b) sin (2tan (0.1)) c) cos (sin -' (-;) + cas -' (3) (4) (12 marks) Find the given limits: Ver + 43 (a) lim I-+ +oo V4" + 2(37) (b) lim vresin(x/2) :x2 + 2x - 3 (c) lim T--34 x+3 (d) lim tan 1 (23 - I) (5) (6 marks) Find horizontal and vertical asymptotes of the given functions: (a) f(x) = e-7 + 307 + 1 (b) g(x) = Vr + 2 (6) (5 marks) Use the Intermediate Value Theorem to show that the equation 25-213-x-1 = 0 has at least two real roots. (7) (5 marks) Find the values of A and B such that the given function is continuous everywhere. [Ae + x :20 f(x) = 1 23 - Bcos (ma) +1 -3