Prob. # 3: Consider the piecewise function x3+1 if x 50 f (x) = -x+2 if 0

Prob. # 3: Consider the piecewise function if x SO if x-2 a) (6 points) Find lim f(x) algebraically Is f (x) continuous at x = O? Give reasons. Is f (x) differentiable at x = 0? Give reasons. b) (6 points) Find lim f (x) algebraically Is f (x) continuous at x = 2? Give reasons. Is f (x) differentiable at x = 2? Give reasons. c) (8 points) Sketch the graph off (x).