CONCORDIA UNIVERSITY Department of Mathematics & Statistics Course Number Sections Mathematics 203 All Examination Date Pages Final December 2017 3 Instructors: J. Brody, X. Gao, U. Mgbemena Course Examiners B. Rhodes, N. Rossokhata, S. Vikram A. Atoyan & H. Proppe Special Only approved calculators are allowed. Instructions: Show all your work for full marks. MARKS [9] 1. (a) Solve for a : 10g2(x - 4) + log2(x + 2) = 2 10g2 4 (b) Given the function f = 1 + In(23 - 8), find the inverse function f-1, the domain and the range of f and the domain and the range of f-1. [6] 2. (a) Calculate both one-sided limits at x = 2 where the function f ( 20 ) = = 20 2 + 2 - 6 120 - 21 is undefined. (b) Is it possible to define f at x = 2 to make f(x) continuous everywhere? Explain. [5] 3. Find all horizontal and all vertical asymptotes of the function f (2) = "V 4x2 + 2x + 1 + 2.2 202 + 25 [15] 4. Find the derivatives of the following functions (show your work for full marks): (a) f(ac) = (201/2 + 20-1/2 )