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AP Calculus AB Limits Question

Please Include detailed answers and explanations

to only a) and b) of the question

Question is attached in picture

AP Calculus AB Test Booklet Hath Journal Name 1. ND CALCULATOR IS ALLOWED FOR THIS QUESTION. Show all of your work. even though the question may not explicitly remind you to do so. Clearly label any functions. graphs. tables. or other objects that you use. Justications require that you giye mathematical reasons. and that you verify the needed conditions under which releyant theorems. properties. definitions. or tests are applied. Your work will he scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified. answers {numeric or algebraic} need not be simplied. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point Unless otherwise specified. the domain of a function .f is assumed to be the set of all real numbers a for which 1' {a} is a real number. Graphuff The graphs of the functions f and 9 are shown above on the interval 3 5 m 5 5. The graphs consist of line segments, except where 1(a) = sfg} on the interval 0 S a: g 2. (a) Write a difference quotient that best approximates the instantaneous rate of change of 9 at a: = 4.5. '2, Please respond on separate paper, following directions from your teacher. {b} Let h (a) = g (f (2)). Find Eh 1"). Use correct limit notation in your answer. '2' Please respond on separate paper, following directions from your teacher. (c) Let H3) = Hz) +901). Consider a: = -1, :a = 2, and a = 4. At which one of these values does I: have a jump discontinuity? Justify your answer for the jump discontinuity using correct limit notation. '2' Please respond on separate paper, following directions from your teacher. {d} Values of H3) at selected values of 2 are given in the table below. What type of discontinuity does f have at a: = 1 '? Based on the values in the table, what is a reasonable estimate for 53" (3) ? Give a reason for your answer. \"mum-Imm f[:s) 2.631 2.628 2.626 2.623 2.621 Undened 2.615 2.613 2.610 2.607 2.605 '2' Please respond on separate paper, following directions from your teacher