MATA30H3 Study Guide - Midterm Guide: Maxima And Minima, Scilab, Mean Value Theorem

1. (18 pts) The graph of a function f, defined on (-0, +o), is given in the figure below. - - y = f(x) - - - - - - N - - 4 A -2-1 144 -1 - - - - - - - -- - - -- Use the graph of f to answer questions (a)-(f) below. (a) Determine the value or write "does not exist". i. f(-3) = -2 ii. f(0) = 1 (b) Determine the limit or write "does not exist" (DNE). Write "does not exist" only if a limit does not exist and is not too or -0. i. lim f(x) = 0 iv. lim f(x) = +00 X- 3 x2 ii. lim f(x) = -4 v. lim f(x) = -0 X- 0- x -00 iii. lim f(x) = DNE vi. lim f(x) = -2 x0 x++00 (C) MULTIPLE CHOICE! Circle ONLY one answer! Find a number a for which the following statement is true (the function f is shown above): STATEMENT: The function f is continuous at a, and lim f(x) = 0. i. a=-3 iii. a=0 V. a=3 ii. a = -2 iv. a = 2 vi. Such a number does not exist. (d) Determine the largest intervals of continuity of f. Use interval notation to write your answer. (-0, -3), (-3,0), (0, 2), (2, +00) (e) Write the equation(s) of all vertical asymptotes of f. Write "none" if appropriate. x= 2 (f) Write the equation(s) of all horizontal asymptotes of f. Write "none" if appropriate. y = -2

3. (20 pts) Let f be a differentiable one-to-one function on the interval (0,4) with the particular values of f and f' given in the table below, and let f-1 be the inverse function of f. Let g be the function given by the graph below. y y=g(x) 12 2 3 5 1 2 3 4 5 6 34-2 For (a), (b), and (c), circle the correct choice. lim 8(3+h) – g(3) h iii. 5 V. -2 vi. does not exist vii. none of the previous choices iv. O (b) dip [6^x +2)/(x) at x = 3 iii. 1 V. -1 vii. none of the previous choices iv. 0 vi. does not exist (0) [r_w) at x = 2 V. vii. none of the previous choices iv. I vi. does not exist (d) Consider the curve given by xey + y = f(x) - 1. Use implicit differentiation to computed at the point (2.0). Show your work.