Barrons AP Calculus - David Bock

The graph of f is shown above. We observe that f is not continuous at x = −2, x = 0, or x = 2. At x = −2, f is not defined. At x ...

left at x = 5.) FIGURE N2–9 In Examples 26 through 31, we determine whether the functions are continuous at the points specified ...

FIGURE N2–10 EXAMPLE 29 Is (x ≠ 2) continuous at x = 2? SOLUTION: Note that k(x) = x + 2 for all x ≠ 2. The function is continuo ...

FIGURE N2–12 EXAMPLE 31 Is continuous at x = 2? SOLUTION: g(x) is not continuous at x = 2 since This discontinuity can be remove ...

Note an important special case of the Intermediate Value Theorem: If f is continuous on the closed interval [a,b], and f (a) and ...

2. (A) 1 (B) 0 (C) −4 (D) −1 (E) ∞ 3. (A) 0 (B) 1 (C) (D) ∞ (E) none of these (A) 1 (B) 0 (C) ∞ (D) −1 (E) nonexistent ( ...

(E) nonexistent 7. (A) −∞ (B) −1 (C) 0 (D) 3 (E) ∞ 8. (A) 3 (B) ∞ (C) 1 (D) −1 (E) 0 9. (A) −1 (B) 1 (C) 0 (D) ∞ (E) none of the ...

(D) = 5 (E) does not exist (A) = 0 (B) (C) = 1 (D) (E) does not exist The graph of y = arctan x has (A) vertical asymptotes ...

16. (A) ∞ (B) 1 (C) nonexistent (D) −1 (E) none of these Which statement is true about the curve (A) The line is a vertical as ...

(E) 1 21. (A) 1 (B) 0 (C) ∞ (D) nonexistent (E) none of these Let Which of the following statements is (are) true? I. exists I ...

Then f (x) is continuous (A) except at x = 1 (B) except at x = 2 (C) except at x = 1 or 2 (D) except at x = 0, 1, or 2 (E) at ea ...

If [x] is the greatest integer not greater than x, then is (A) (B) 1 (C) nonexistent (D) 0 (E) none of these (With the same not ...

32. (A) equals 0 (B) equals 1 (C) equals 2 (D) does not exist (E) none of these The function f is defined on [−1,3] (A) if x ≠ ...

(B) x = 1 (C) x = 2 (D) x = 3 (E) none of these On which of the following intervals is f continuous? (A) −1 ≤ x ≤ 0 (B) 0 < ...

(B) I only (C) III only (D) I and III only (E) All of them CHALLENGE If then y is (A) 0 (B) (C) (D) (E) nonexistent Questions ...

(B) 1 only (C) 2 only (D) 1 and 2 only (E) −1, 1, and 2 Which statements about limits at x = 1 are true? I. exists. II. exists. ...

CHAPTER 3 Differentiation Concepts and Skills In this chapter, you will review derivatives as instantaneous rates of change; es ...

the (instantaneous) rate of change of f at point a. Geometrically, the derivative f ′(a) is the limit of the slope of secant PQ ...

FIGURE N3–1b The second derivative, denoted by f ′′(x) or or y ′′, is the (first) derivative of f ′(x). Also, f ′′(a) is the sec ...

C. THE CHAIN RULE; THE DERIVATIVE OF A COMPOSITE FUNCTION Formula (3) says that This formula is an application of the Chain Rule ...