By Maxine Lifshitz
Offers a whole assessment of subject matters incorporated within the university Board AP Calculus AB and Calculus BC direction descriptions and may aid scholars advance the abilities and techniques had to be successful on either the Calculus AB and Calculus BC tests.
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Extra resources for Amsco's AP Calculus AB BC: Preparing for the Advanced Placement Exams
Finding the range of a simple function such as a line or parabola is a straightforward process. An arbitrary function may have maximum and minimum values that are difficult to locate. In some cases, therefore, finding the range may require using the methods of calculus. Functional Notation The value of a function f(x) at x ϭ 2 is denoted f(2). If the function is f(x) ϭ 4x ϩ 1, for example, then f(2) ϭ 4(2) ϩ 1 ϭ 9. Similarly, f(a) ϭ 4a ϩ 1, and f(x Ϫ 1) ϭ 4(x Ϫ 1) ϩ 1 ϭ 4x Ϫ 3. Symmetry of If a function f(x) is even, its graph is symmetric with respect to the a Function y-axis.
X2 Ϫ 1 (D) 100 (E) does not exist Evaluating Limits as x Approaches ; q 47 Free-Response Questions A graphing calculator is required for some questions x 1. (a) Graph f(x) ϭ 2 . x Ϫ1 (b) Use the graph to determine: • lim f(x) + x→1 lim f(x) x S Ϫq 2. 4 Special Limits: lim sin x and lim x x→0 x→0 One of the first theorems in many calculus books proves the following geometrically: lim x→0 sin x x ϭ 1. 1. Enter values in the TABLE that approach 0 from the positive side and from the negative side. The corresponding values of the function will be closer and closer to 1.
E) Does f(x) have an inverse? If yes, find the inverse and graph it. If not, explain why. 2. (a) Use the graph of f(x) below to find: • lim f(x) Ϫ xS2 • lim f(x) ϩ xS2 • lim f(x) xSq • lim f(x) x S Ϫq (b) Does f(x) have an inverse? Explain. 2 Evaluating Limits as x Approaches a Finite Number c To evaluate a limit algebraically as x approaches a finite number c, substitute c into the expression. 1. If the answer is a finite number, that number is the value of the limit. 0 2. If the answer is of the form , we have an indeterminate form.
Amsco's AP Calculus AB BC: Preparing for the Advanced Placement Exams by Maxine Lifshitz