1. State the limit for each of the following using the graph. -3 -2 -2 a. lim_f (x) b . x--3 lim _f (x) C. lim_f (x) x--3+ x--1 d. lim f(x) e. lim f (x) f. x--1 x-2- lim f(x) x-2+ 2. State whether the function in question 1 is continuous or discontinuous at the x = -3, -1, and 2. 3 Sketch the following functions. Determine whether the function is continuous or discontinuous. State the value(s) of x where there is discontinuity. Justify your answers. x, x5 -4 a. f (x) = 5, -4 3 12 - x2, x>-1 4 Evaluate each limit, if it exists. If the limit does not exist, explain why. a. lim 8 b. lim * - 9 X-6 x--3x+5 C. lim x--5 x +5 d. lim V12 - x +X 5. Evaluate each limit, if it exists. a lim x2 - 4 b. lim 3x2 - x -2x x--2 x+2 x-0x+5x2 C. lim - x--0x2-4x d. lim x2+ 4x -5 e. 2x2 - 5x - 3 lim 2 f. lim 3x2+ 11x - 4 x--5 25-x2 x-+3 x2-x-6 x-+3 x2+3x-4 6. Evaluate each limit, if it exists. Hint: use Rationalization. a. lim V9 + x - 3 b. lim V3 - x - Vx + 3 x-0 x Calculus and Vectors Lesson 2 7. What is true about the graph of y = b(x) if lim_b(x) = lim_b(x) = 7, but b(11) # 7? x-11 x-11+