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

By Maxine Lifshitz

Presents an entire evaluate of issues incorporated within the collage Board AP Calculus AB and Calculus BC path descriptions and may support scholars enhance the abilities and techniques had to prevail on either the Calculus AB and Calculus BC checks.

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Example text

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. Thus, x ϭ (y Ϫ 2)2. This is the equation of a parabola, but there is still a restriction on the values of x and y, depending on the values of t that are used, say t between 0 and 3 or t between Ϫ3 and 3.

Lim␲ x ϭ xS 2 (A) 0 (B) 1 2 (C) ␲ ␲ (D) 2 (E) does not exist sin 2x 4. lim x cos x ϭ x→0 Ϫ1 0 1 2 does not exist x2 ϩ 1, x Ͻ 2 5. f(x) ϭ e 4, xϾ2 lim f(x) ϭ (A) (B) (C) (D) (E) x → 2Ϫ (A) (B) (C) (D) (E) 0 2 4 5 does not exist x 6. The vertical asymptote of f(x) ϭ has xϪ1 equation (A) x ϭ 0 (B) x ϭ 1 (C) y ϭ 0 (D) y ϭ 1 (E) There is no vertical asymptote. x 7. The horizontal asymptote of f(x) ϭ is xϪ1 (A) x ϭ 0 (B) x ϭ 1 (C) y ϭ 0 (D) y ϭ 1 (E) There is no horizontal asymptote. 8. The vertical asymptote of f(x) ϭ 4 is xϩ1 (A) x ϭ Ϫ1 (B) x ϭ 0 (C) y ϭ Ϫ1 (D) y ϭ 0 (E) There is no vertical asymptote.

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. Since x S ϩq and the coefficients of the highest degree terms are both positive, we can also say that the limit is ϩq. Evaluate lim 2 x S q 7x EXAMPLE 5 Evaluate lim x x S Ϫq Solution . ϩ1 x ϭ lim "x2 ϩ 1 x S Ϫq "x2 lim x S Ϫq 1 x2 ϩ 1 A x Since x S Ϫq, x 6 0 and therefore, x2 1 ϭ Ϫ1 1 lim ϭ lim Ϫ lim Ϫ 2 ϩ 1 ϭ xS x 2 x S Ϫq x S Ϫq Ϫq A x ϩ1 1 ϩ 12 x A Ϫ "x2 Q Exercises Multiple-Choice Questions No calculator is allowed for these questions.

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