Section 1.5 1. Find values of a and b so that the following function is continuous everywhere. [5p] ax2 + b for x 2. 2. Use the Intermediate Value Theorem to show that the following equation [6p] 23 = has at least one real solution. Section 1.6 3. Evaluate the following limits. 4x - 3 (a) [3p] x- -00 V25x2 + 4x (b) lim (VArt + 9x - 2x2) [3p] x-+00 4. Sketch the graph of an example of a function f that satisfies all of the following conditions: [7p] . f(0) = 3 . lim f(x) = -00 . lim f(x) = 00 x - -00 x-4+ . lim f(x) = 4 lim f(a) = 2 . lim f(x) = -00 . lim f(x) = 3 x-0+ x-+4- 5. Find the horizontal and vertical asymptotes of each curve using limits. (a) f(a) = 2x2 +x - 1 [6p] (b) F(x) = x-9 [6p] x2 + x - 2 Vac2 + 9