Amsco's AP Calculus AB BC: Preparing for the Advanced by Maxine Lifshitz

By Maxine Lifshitz

Offers a whole evaluation of themes incorporated within the collage Board AP Calculus AB and Calculus BC path descriptions and should support scholars advance the abilities and methods had to be successful on either the Calculus AB and Calculus BC assessments.

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Extra info for Amsco's AP Calculus AB BC: Preparing for the Advanced Placement Exams

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2x Ϫ 2 (A) y ϭ 0 (B) x ϭ 1 2 1 (C) y ϭ 2 (D) x ϭ 1 (E) x ϭ ; 1 22. Find f(2) for f(x) ϭ b (A) (B) (C) (D) (E) x2 ϩ 4, x 6 0 . 3 Ϫ x, x Ն 0 1 3 4 8 does not exist 23. Which of the following graphs shows a function that is continuous for all real numbers? (A) y x y (B) Ϫ 4x ϩ 4 ϭ 4x2 Ϫ 1 (A) 1 4 (B) 1 (C) 4 (D) 8 (E) does not exist 20. Find the equation of the vertical asymptote x of f(x) ϭ . 4x ϩ 8 (A) y ϭ 1 4 (B) y ϭ Ϫ2 (C) x ϭ Ϫ2 (D) y ϭ 2 (E) x ϭ 2 56 Chapter 3 • Limits and Continuity x (C) y x (D) 3.

A) Write a function f(x) that has a removable discontinuity. (b) Write a function g(x) that has a nonremovable discontinuity. Chapter Assessment Multiple-Choice Questions No calculator is allowed for these questions x 1. lim ϭ x→2 x Ϫ 2 (A) Ϫ1 54 Chapter 3 • Limits and Continuity (B) (C) (D) (E) 0 1 2 does not exist 2. lim x→5 (A) (B) (C) (D) (E) xϪ5 ϭ x2 Ϫ 25 Ϫ1 0 1 10 1 does not exist sin x 3. lim␲ x ϭ xS 2 (A) 0 (B) 1 2 (C) ␲ ␲ (D) 2 (E) does not exist sin 2x 4. lim x cos x ϭ x→0 Ϫ1 0 1 2 does not exist x2 ϩ 1, x Ͻ 2 5.

Calculator Note To see if a function is even or odd using the calculator, enter the function in Y1. Then enter Y1(Ϫx) into Y2. Now graph Y1 and Y2. If the function is even, then Y1 and Y2 are the same function, and only one function will appear on the graph. If the function is odd, then Y1 and Y2 are opposites, and two opposite functions will appear on the graph. 3 Properties of Functions 25 EXAMPLE 4 xϩ2 . x2 Ϫ 1 The vertical asymptotes are found by solving x2 Ϫ 1 ϭ 0. Find the equations of the vertical asymptote(s) of y ϭ Solution The solutions are x ϭ 1 and x ϭ Ϫ1.

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