1. Determine the following limits, if they exist. Show your work. [10K] lim X 1 1 a) $90 1+V14x2 b) lim (2) e) lim X N x-3 x-2 (x-2) VI+x-1 lim d) c)lim x-5x2-5x3. Sketch a graph of any function that would satisfy all the given conditions below: [3C] All tangent lines to this graph have a negative slope lim f (x) = 3 and lim f (x) = -1 x-2+ x-2 lim f (x) = 0 and lim f(x) = -co X--3+ x--3 lim f (x) = 00 X--00 4. State whether the function is continuous everywhere. Show all your steps. If the function is not continuous, also state which continuity condition is not satisfied and at which point. [3A, 1C] f (ac) = x - 2 if x 2 0 -(x+3) ifx 3 g(a) = if x = 3 x- - bata ifa