Math 21,Spring 2016 1 Worksheet #2 Associated with material covered in sections 1.5, 1.6 in Stewart's Calculus 1. (a) True or False. As x increases to 100, f (x) = 1/x gets closer and closer to 0, so the limit as x goes to 100 of f (x) is 0. Justify your answer. (b) True or False. lim f (x) = L means that if x1 is closer to a than x2 is, then xa f (x1 ) will be closer to L than f (x2 ) is. Justify your answer with an argument or counterexample. (c) True or False. If lim f (x) = and lim g(x) = , then lim [f (x) g(x)] = 0. xa 2. Find asymptotes of f (x) = 3. Given that lim f (x) = 4 x2 (a) lim x2 xa xa 1 1 + sin x lim g(x) = 2, nd: x2 f (x) 3f (x) x2 g(x) (b) lim 4. Find the requested limits, if they exist. If they do not exist, explain. xa xa |x a| lim 9 + 4x x4 2 x lim x2 2x 1 x 51 lim x5 x5 2x(x 1) lim x1 |x 1| (a) lim (b) (c) (d) (e) 5. Find the following limits. x2 2x 35 x5 x+5 2 x 3 (b) lim x 3 x 3 25 + x 5 (c) lim x0 x x3 4x (d) lim x2 x 2 (a) lim