By Maxine Lifshitz
Offers a whole evaluation of issues incorporated within the collage Board AP Calculus AB and Calculus BC direction descriptions and should support scholars increase the talents and techniques had to be successful on either the Calculus AB and Calculus BC tests.
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Extra info for Amsco's AP Calculus AB BC: Preparing for the Advanced Placement Exams
Factor the numerator and the denom0 3x Ϫ 1 inator and simplify the expression to . xϩ1 3x2 Ϫ 4x ϩ 1 (3x Ϫ 1)(x Ϫ 1) 3x Ϫ 1 ϭ ϭ xϩ1 x2 Ϫ 1 (x ϩ 1)(x Ϫ 1) Now substitute x ϭ 1 into the simplified expression. The result is 1. EXAMPLE 5 Evaluate lim x → 25 "x Ϫ 5 . x Ϫ 25 0 Solution Substitute x ϭ 25 into the expression. The result is , an inde0 terminate form. Since the numerator has a square root, rationalize the numerator by multiplying the numerator and the denominator by the conjugate "x ϩ 5. Multiply out the conjugates in the numerator, but leave the denominator in factored form.
A) ln x2 (B) ex2 Ϫ x (C) ex2 Ϫ x2 (D) ex3 ϩ 1 (E) 2 1 x Ϫ4 4. Find the domain of f(x) ϭ ln(tan x) on the interval 3Ϫ, 4 . (A) all x in (Ϫ, ) (B) all x in (0, ) (C) all x in Q0, R 2 (D) all x in QϪ, Ϫ R and Q0, R 2 2 (E) all x in BϪ , R 2 2 (x Ϫ 1)2 has x2 Ϫ 1 a hole at x ϭ Ϫ1 holes at x ϭ Ϫ1 and x ϭ 1 vertical asymptotes at x ϭ 1 and x ϭ Ϫ1 a horizontal asymptote at y ϭ Ϫ1 a hole at x ϭ 1 and a vertical asymptote at x ϭ Ϫ1 5. f(x) ϭ (A) (B) (C) (D) (E) 6. f(x) is an odd function and the graph of f contains the point (6, 5).
This is the procedure for finding inverses of functions such as y ϭ x2 and y ϭ sin x. The graph of the inverse of a function is the reflection of the graph of the function (on its restricted domain) in the line y ϭ x. The equation of the inverse of a function can be found by exchanging x and y in the equation of the function, and then solving for y. The domain of the inverse is the range of the function, and the range of the inverse is the domain of the function. 28 Chapter 2 • Functions and Their Properties Calculator Note The TI-83 and TI-89 calculators have a built-in draw inverse feature.
Amsco's AP Calculus AB BC: Preparing for the Advanced Placement Exams by Maxine Lifshitz
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