• You have to show all your work, including intermediate steps, and explain how you reached your conclusion.

A. Apply the rigorous (" ") definition

1. lim_x1 x ² + 1

2. Find , such that |x| < implies |x ² 2x| < 10²

B. Left- and Right- Limits/Continuity: Choose the constant c such that the the piecewise defined functions are continuous.

1. 1. lim_x2 f(x) where f(x) = { cx + 7 x < 2

cx² 5 x > 2

2. lim_x0 f(x) where f(x) = {cx+11 x < 0

e ^x x > 0

3. lim_x0 f(x) where f(x) = {x211 x<0

1+xecx x>0