5. Let f(x) = [x| + [x] where |x| is the absolute value of x and [x] is the greatest integer function in x. a. Draw the graph of f by hand for x in [0, 2]. b. For which values of a in (0, 2) does lim f(x) exist? c. For which values of x in (0, 2) is f continuous at x? Explain using the definition of continuity. 6. a. State the domain of f (x) = = VX2-4 x2+x-12 - in interval notation. b. Use any of Theorems 4, 5, 7 and 9 on continuity to show that the function fabove is continuous at each point of its domain. 7. a. Use the intermediate value theorem to show that there is a root of f (x) = x*+ 1 --in (, 1). Note that you must show the hypothesis of the theorem are satisfied before you can apply the theorem. b. By using the theorem repeatedly find the root to two decimal places. 8. a. Find f'(x) for f(x) = v4x + 1 using the definition of the derivative. b. Find an equation of the tangent line to fat x = 19. a. Copy the graph below of the function fby hand and directly below it, sketch its derivative by hand. b. Sketch the graph of a single function f that satisfies all of the following conditions: i) lim f(x) = -2 ii) lim f (x) = X-4-00 X-100 0 iii) lim f(x) = 00 X--3 iv) lim f(x) = -00 v) lim f(x) = -2 vi) fis x4+-3 continuous from right at 3