By Maxine Lifshitz

ISBN-10: 1567655629

ISBN-13: 9781567655629

Offers an entire overview of subject matters incorporated within the collage Board AP Calculus AB and Calculus BC direction descriptions and may aid scholars strengthen the abilities and methods had to be successful on either the Calculus AB and Calculus BC assessments.

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

Example text

Solution Press o, and enter X1T ϭ t2 and Y1T ϭ t ϩ 2. Define the window and then press s. Use r to find that the domain for t is [0, 3], the domain for x is [0, 9], and the range for y is [0, 5]. EXAMPLE 2 Using the parametric function from Example 1, go to p and change Tmin ϭ Ϫ3, and press s. Find the domain and range of the graph. Solution Notice that the graph is not that of a function. It is now a relation. The domain of t is [ Ϫ3, 3]. The domain of x is [0, 9]. The range of y is [ Ϫ1, 5]. 6 Parametric Equations 33 By eliminating the parameter t, the set of parametric equations given in Example 1 on page 33, x ϭ t2 and y ϭ t ϩ 2, can be transformed into a single equation in terms of x and y as follows: solve for t in y ϭ t ϩ 2, t ϭ y Ϫ 2, and substitute t into the equation for x, x ϭ t2.

X S 0؊ xS0 Since lim؉f(x) Z lim؊f(x), lim f(x) does not exist. xS0 xS0 xS0 Exercises 3. lim f(x) ϭ Multiple-Choice Questions A graphing calculator is required for some questions. x ϩ 3, x Ͻ 0 In Exercises 1Ϫ5, use f(x) ϭ e . x Ϫ 3, x Ն 0 1. limϪ f(x) ϭ x→0 (D) 3 (E) does not exist (A) Ϫ2 (B) Ϫ1 (C) 0 (D) 1 (E) does not exist 5. lim f(x) ϭ x → Ϫ2 2. limϩ f(x) ϭ (A) Ϫ3 (B) 0 (C) 1 x→0 (A) Ϫ3 (B) 0 (C) 1 (D) 3 (E) does not exist x→1 x→0 (A) Ϫ3 (B) 0 (C) 1 (A) Ϫ3 (B) 0 (C) 1 4. 5 (D) 3 (E) does not exist Evaluating Limits of a Piecewise-Defined Function 51 2.

X→0 x→0 Exercises Multiple-Choice Questions No calculator is allowed for these questions. sin 7x 1. Evaluate lim . 7x x→0 (A) 0 (D) 7 1 (B) (E) indeterminate 7 (C) 1 2. Evaluate lim x→0 sin 7x x . 4 sin x 1 Ϫ cos x Special Limits: lim x and lim x x→0 x→0 49 3. Evaluate lim x→0 sin x . 7x Free-Response Questions No calculator is allowed for these questions. (A) 0 (B) 1 7 (C) 1 (D) 7 (E) indeterminate 1. Use the special trigonometric limits to find the value of each of the following: tan x (a) lim x x→0 (b) lim x→0 sin x 4.

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


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