1. State the limit for each of the following using the graph. -Not -2- a. lim f(x) b. x--3 lim_f (x) C. lim f(x) x--3+ x--1 lim _f(x) e. x--1+ lim f(x) f . 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 b. S3x + 1, x5-1 f ( x) = 12 - x2 , x>-1 Evaluate each limit, if it exists. If the limit does not exist, explain why. a. lim 8 b. lim x2 - 9 x-+6 x--3x+5 C. lim 6x + 2 x--5 x +5 d. lim V12 - x 5 . Evaluate each limit, if it exists. a. x2 - 4 lim b. lim 3x2 - x x--2 x+2 x-ox+5x2 C. lim - -2x x--0x2-4x lim x2+ 4x - 5 2x2- 5x - 3 x--5 25-x2 e. lim f. lim 3x2+ 11x - 4 x-+3 x2-x-6 x2+3x-4 6. Evaluate each limit, if it exists. Hint: use Rationalization. a. lim V9 + x - 3 x-0 x b. lim V3 - x - Vx + 3 X-0 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+