Math 210 Extra credit Name: (Print) a You are required to show your work on each problem. (65 pts) 1. (16 pts) Consider the graph below of the function fix). Answer the following questions. (a) (4 pts) Determine the intervals over which f(x) is continuous. (b) (4 pts) At what points in its domain does f have a non -removable discontinuity? Explain why. (c) (3 pts) Determine if the following limit exists. If it does compute it. If not, explain why. .2229? m (d) ( 2 pts) Determine if the following limit exists. If it does compute it. If not, explain why -1 lim x-o+ f(x) (e) (3 pts) Find the following limit. lim (-Vf (x)) x - - 1 2. (5 pts) If lim f(x) = 9 and lim g(x) = 0, evaluate the following limit. lim (f (x)+92+3)3. (24 pts) Consider the following limits. If the limit exists, find it. If limit is co, -co, or does not exist, give a reason why. (a) (5 pts) (x2 + 4x + 3) lim x--3- (x2 + 6x + 9) (b) (5 pts) -4x + 12 lim x--0ov5 + 25x2 (c) (3 pts) lim - x-o+ Inx (d) (4 pts) 3x2 - 5x - 6x2022 lim X- -00 1 + 6x2023 3(e) (3 pts) lim (x + |x - 1| +4) (f) (4 pts) sinx lim x-+0ox2+1 4. (3 pts) Use limits to determine if the following function has a horizontal asymptote. If so, find it. f(x) = -e3-x 5. (5 pts) Find the value of a that makes the function f continuous. - x3 + a, f (x) =1-3x -20, x2 - 1