1. Find the following limits without using a graphing calculator or making tables. (a) x 3 3x 2 2 x x 2 x 2 lim (b) lim x 3 x 3 x 2 6 x 9 (c) lim 2 xh 2 6 x 2 h 3 h 0 h2 2. For each piecewise linear function, graph the function and find: lim x 4 f x f x lim x 4 x 2 (a) f x x 2 lim f x x 4 if x 4 if x 4 2 (b) f x 2x 4 if x 3 if x 3 3. For each piecewise linear function, graph the function and find: lim x 3 f x lim x 3 f x (a) f x x 3 1 lim x 3 f x (b) f x x 2 4. Find the value of k which makes the following piecewise linear function continuous: (a) kx 1 if x 1 f x if x 1 2k if x 2 kx 2 (b) f x kx 1 if x 2 5. Determine whether each function is continuous or discontinuous. If the function is discontinuous, state where it is discontinuous. (a) f x x2 1 f x x 3 (c) x 1 (b) f x x 3 1 x 2 2 x 1 x3 x2 x2 (d) f x 2 x 4 x4 x 2x 6. Use the definition of derivative as limit of a difference quotient to find the derivative of each function given, at x = x0 . (a) f x x 2 2 (b) f x 1 4x 1 (c) f x 3 x 1 2 7. Use the results in Problem 5. above to find an equation of the tangent line to the graph of each f(x) at the point indicated. (a) f x x 2 1, x 1 (b) f x 1 , 4x 1 x 3 (c) f x 3 x 1 2 , x 2