Assignment 2 Module: Limit of a Function Limits at infinity, derivatives, rates of change 1. (20 pts) Sketch the graph of an example of a function f that satisfies all of the given conditions. f(0) = 0 lim f (x) = 00 lim f (x) = -2 x-1 x-1 lim f (x) = -0o lim f(x) = -2 x- -00' x-+00" 2. (24 pts) For the function g whose graph is given, state the following: a. lim g(x) X-00 b. lim g(x) X - -00 C. lim g (x) -1 X-0 A d. lim g(x) x-2- . lim, g(x) x-2+ f. The equations of asymptotes. 3. (30 pts) Find the limit or show that it does not exist. a. lim - -2 X-+00 3x+7 b. lim 6t2+t-5 t--00 9-2t2 c. lim - t+3 t-co V2t2-1 4. (12 pts) Find an equation of the tangent line to the curve y = 2x2 - 5x + 1 at the point (3,4). 5. (14 pts) A cliff diver plunges from a height of 100 ft above the water surface. The distance the diver falls in t seconds is given by the function d(t) = 16t2ft. a. After how many seconds will the diver hit the water? b. With what velocity does the diver hit the water