By William Ma
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Additional info for AP Calculus AB
Unless otherwise indicated, the domain of a function f is the set of all real numbers. The use of a calculator is not permitted in this part of the test. ∫ 4 1 1 V(t) dx. x (feet/second) 1. Evaluate π 2. If f(x) = −2csc(5x), find f ′ . 6 x −4 . 2x 2 3. Evaluate xlim → −∞ 4. Given the equation y = x − 1, what is an equation of the normal line to the graph at x = 5? 20 V 10 0 2 4 6 t (seconds) 8 –10 5. The graph of f is shown in Figure D-1. Draw a possible graph of f ′ on (a, b). Figure D-2 y 10.
And f decreases on (2, 5) and increases on (5, 6), f has a relative minimum at x = 5. as x → −∞, the denominator e−2x → ∞ However, the denominator increases at a xe 2 x = 0. much greater rate and thus xlim → −∞ (d) Since as x → ∞, xe2x increases without bound, f has no absolute maximum value. 5. 5 is the only critical point on an open interval. 5e ( ) = − 2e (c) See Figure DS-16. Since f′ is increasing on the intervals (−4, 0) and (4, 6), f″ > 0 on (−4, 0) and (4, 6). (d) A change of concavity occurs at x = 0 and at x = 4.
Card if your school or the test site requires it. Your Social Security number Your school code number if the test site is not at your school A simple snack if the test site permits it. (Don’t try anything you haven’t eaten before. ) A light jacket if you know that the test site has strong air conditioning Do not bring Wite Out or scrap paper. TIPS FOR TAKING THE EXAM General Tips • Write legibly. • Label all diagrams. 0267-02/Part II 12/18/2001 17:23 Page 16 16 • What You Need to Know About the AP Calculus AB Exam • Organize your solution so that the reader can follow you line of reasoning.
AP Calculus AB by William Ma