1 . A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax. 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. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be 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 simplified. 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 f (x) is a real number. Let f be the function defined by f(x) = cos (Vx). (a) Approximate the definite integral / f(x) dx using a midpoint Riemann sum with the subintervals |1, 1.6], [1.6, 2], and [2, 3]. Show the work that leads to your answer. Please respond on separate paper, following directions from your teacher. (b) Approximate the definite integral / f(x) dx using a trapezoidal sum with the subintervals [1, 1.6], [1.6, 2], and [2, 3]. Show the work that leads to your answer. Please respond on separate paper, following directions from your teacher. (c) It is known that f'(x) = sin (VI) cos ( VI) 2VI and f" (x) = sin (VI) AIVI 4x . Would a trapezoidal sum approximation for r / f( x) dx overestimate or underestimate the value of / f(x) da ? Give a reason for your answer.nit 6 Progress Check: FRQ Part A absolute minimum value of fand the absolute maximum value of fon the closed interval 0 _ x - 7. Justify your answers. Please respond on separate paper, following directions from your teacher. (c) Find / g(x) dx. Please respond on separate paper, following directions from your teacher. (d) Find the value of / x f'(g(x) ) dx. Please respond on separate paper, following directions from your teacher