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

By Maxine Lifshitz

ISBN-10: 1567655629

ISBN-13: 9781567655629

Presents an entire overview of subject matters integrated within the university Board AP Calculus AB and Calculus BC direction descriptions and should support scholars increase the talents and techniques had to be triumphant 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

1Ϫ1 x 3 0 Solution Substituting x ϭ 3 into the expression gives the result , an 0 indeterminate form. In this case, simplify the complex fraction by multiplying the numerator and the denominator by the least common 1 denominator of 1 x Ϫ 3 , which is 3x. a 3x(x Ϫ 3) 3x(x Ϫ 3) 3x x Ϫ 3 ϭ b ϭ 3x 1 Ϫ 1 3Ϫx 1 x 3 3x a 1 x b Ϫ3x a 3 b This produces the following result: lim x→3 3x(x Ϫ 3) . 3Ϫx Simplifying further as shown reduces the expression to lim (Ϫ3x). x→3 3x(x Ϫ 3) 3x(x Ϫ 3) Ϫ3x( Ϫ x ϩ 3) ϭ Ϫ3x ϭ ϭ 3Ϫx Ϫx ϩ 3 Ϫx ϩ 3 Now substitute x ϭ 3, and the value of the limit is Ϫ9.

A) Sketch the graph of y ϭ ϪeϪx. State its domain and range. (b) On the calculator, enter y DRAW 8: DrawInv Y1, and copy the inverse onto your graph. (c) Solve algebraically for the inverse of y ϭ ϪeϪx. (d) Enter the equation of the inverse in Y2. Graph it and examine the symmetry to check that it is in fact the equation of the inverse. 2. (a) Find the domain and range of the function y ϭ "x Ϫ 2 ϩ 1, and sketch the graph. (b) Find the domain and range of the inverse, and solve algebraically for the equation of the inverse.

GRAPHICALLY Since it is symmetric with respect to the origin, the function is odd. Choose several x-values to see if either f(Ϫx) ϭ f(x), or f(Ϫx) ϭ Ϫf(x). It should appear that f(Ϫx) ϭ Ϫf(x). To prove this, note that ALGEBRAICALLY e(Ϫx)2 ex2 ex2 f(Ϫx) ϭ Ϫx ϭ Ϫx ϭ Ϫ x , which is Ϫf(x). Therefore, f(x) is odd. 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.

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