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

By Maxine Lifshitz

ISBN-10: 1567655629

ISBN-13: 9781567655629

Offers a whole assessment of issues integrated within the university Board AP Calculus AB and Calculus BC direction descriptions and should support scholars strengthen the talents and methods had to be triumphant on either the Calculus AB and Calculus BC checks.

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Sample text

2 Evaluate lim xSq EXAMPLE 2 Evaluate lim xSq 46 Chapter 3 • Limits and Continuity 2x2 ϩ x ϩ 1 . 5x2 Ϫ x ϩ 5 Solution Since this is a rational function and the degree of the numerator equals the degree of the denominator, the limit is the ratio of the leading coefficients, 2 . 5 EXAMPLE 3 x2 ϩ x ϩ 4 . 5x3 ϩ 7x Solution Since this is a rational function and the degree of the numerator is less than the degree of the denominator, the limit is 0. Evaluate lim xSq EXAMPLE 4 6x3 . ϩ 1000x Ϫ 9 Solution Since this is a rational function and the degree of the numerator is greater than the degree of the denominator, the limit does not exist.

Lim f(x) ϭ 8. lim f(x) ϭ 2. limϪ f(x) ϭ (A) (B) (C) (D) (E) (C) 2 (D) e (E) does not exist ex, x Ͻ 1 . ln x, x Ն 1 6. limϪ f(x) ϭ x→1 (A) 0 (B) 1 (a) Find the value of p so that f(x) is continuous at x ϭ Ϫ1. (b) Using the value of p found in part (a), sketch the graph of f(x). 2x Ϫ 3, x Z 2 has a removable dis0, xϭ2 continuity. Redefine f(x) so that it is continuous at x ϭ 2. 3. f(x) ϭ e 4. (a) Write a function f(x) that has a removable discontinuity. (b) Write a function g(x) that has a nonremovable discontinuity.

If the point with coordinates (3, k) is on the line 2x Ϫ 5y ϭ 8, find the value of k. (A) Ϫ 14 5 3 (B) Ϫ 5 (C) Ϫ 2 5 2 (D) 5 (E) 14 5 5. The equation of the line joining the points (Ϫ1, 2) and (5, 6) is (A) 2x Ϫ 3y ϭ 8 (B) 2x Ϫ 3y ϩ 8 ϭ 0 (C) 2x ϩ 3y ϭ 8 (D) 2x ϩ 3y ϩ 8 ϭ 0 (E) y ϭ 2 x 3 6. Which of the following are the equation of a line? I y ϭ 2x Ϫ 5 II y ϭ x2 Ϫ 5 III 2y Ϫ 3x ϭ 0 (A) I only (B) III only (C) I and III (D) II and III (E) I, II, and III Free-Response Questions No calculator is allowed for these questions.

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


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