Part II. Long Questions (50 marks) Write all your solution to the questions of this part in the answer book provided separately. For full credits, you should give concise and precise reasoning to your solution; and show your steps clearly. 26. (16 marks) Let f (x) = cells', I > 0. (a) Determine the intervals of increasing and the intervals of decreasing- (b) Determine the intervals where the graph of f is concave up as well as the intervals where the graph is concave down. (c) Determine all the vertical, horizontal and oblique asymptotes, if any. 27. (14 marks) Let f(x) = rarctanz - arctant dt. (a) Find the second degree Taylor polynomial of f at the reference point a = 1. P.6 of 7 (b) Use the polynomial in part (a) to estimate f(1.1) and find an upper bound for the absolute error committed. You may use the following formula whenever appropriate. - arctan - if a + 0. 28. (20 marks) Let n be a non-negative integer and define In = cach x do = 1 sIn" (a) Evaluate h1. (b) Let n 2 2. Use integration by parts to express cost a csc" I de in terms of Is for some non-negative integer k. Hence, or otherwise, show that In = - 1 n- 1 COST Caches+ - n - 2 7 - 1 In-2. (c) Compute Is and I4