Barrons AP Calculus - David Bock

(E) all reals The domain of is (A) all x ≠ 0, 1 (B) x 2, x ≠ 0, 1 (C) x 2 (D) x 2 (E) x > 2 If f (x) = x^3 − 3x^2 − 2x + 5 ...

(C) g is symmetric to the origin. (D) g is strictly increasing. (E) g is one-to-one. Let y = f (x) = sin (arctan x). Then the r ...

(A) {−2} (B) {0,−2} (C) {0,2} (D) {2} (E) {2,−2} The values of x for which the graphs of y = x + 2 and y^2 = 4x intersect are ( ...

The period of f (x) = is (A) (B) (C) (D) 3 (E) 6 The range of y = f (x) = ln (cos x) is (A) {y | − ∞ < y 0} (B) {y | 0 < ...

(D) {−1,1,2} (E) {−1,−2,2} If the domain of f is restricted to the open interval then the range of f (x) = etan x is (A) the s ...

(B) (C) (D) (E) ln (2 − x) Which of the following functions does not have an inverse function? (A) (B) y = x^3 + 2 (C) (D) (E) ...

BC ONLY Which equation includes the curve defined parametrically by x(t) = cos^2 (t) and y(t) = 2 sin (t)? (A) x^2 + y^2 = 4 ( ...

(D) 4.263 (E) 5.201 BC ONLY ...

CHAPTER 2 Limits and Continuity Concepts and Skills In this chapter, you will review general properties of limits; how to find ...

FIGURE N2–1 However, [x] does have a limit at every nonintegral real number. For example, EXAMPLE 2 Suppose the function y = f ( ...

FIGURE N2–2 SOLUTIONS: (a) so the right-hand limit exists at x = −2, even though f is not defined at x = −2. (b) does not exist. ...

FIGURE N2–3 DEFINITION The function f (x) is said to become infinite (positively or negatively) as x approaches c if f (x) can b ...

EXAMPLE 5 Describe the behavior of near x = 1 using limits. SOLUTION: The graph (Figure N2–5) shows that: FIGURE N2–5 Remember t ...

FIGURE N2–6 DEFINITION The theorems that follow in §C of this chapter confirm the conjectures made about limits of functions fro ...

Horizontal asymptote The line y = b is a horizontal asymptote of the graph of y = f (x) if The graph of (Figure N2–4) has the x- ...

FIGURE N2–7 C. THEOREMS ON LIMITS If lim f (x) and lim g(x) are finite numbers, then: (1) lim kf (x) = k lim f (x). (2) lim[f (x ...

EXAMPLE 10 EXAMPLE 11 EXAMPLE 12 since, by the definition of in §A, x must be different from 3 as x → 3, the factor x − 3 may be ...

EXAMPLE 17 D. LIMIT OF A QUOTIENT OF POLYNOMIALS To find where P(x) and Q(x) are polynomials in x, we can divide both numerator ...

(ii) when then the graph of has no horizontal asymptotes; (iii) when is a horizontal asymptote of the graph of EXAMPLE 21 E. OTH ...

The value of e can be approximated on a graphing calculator to a large number of decimal places by evaluating for large values o ...