Barrons AP Calculus

(D) Use the Rational Function Theorem. The degrees of P(x) and Q(x) are the ...

(B) (B) Because the graph of y = tan x has vertical asymptotes at , the graph ...

. (E) Note that x sin can be rewritten as and that, as . (A) As x → ...

(D) See Figure N2–1. (E) Note, from Figure N2–1, that . (E) As x → ∞, the ...

37. 38. 39. 40. 41. 42. 1. (E) As x → 0−, arctan , so . As . The graph has a jump discontinuity at ...

y′ = x^5 (tan x)′ + (x^5 )′ (tan x). (A) By the Quotient Rule, (6), (B) Since ...

= x − ln(ex − 1), then (E) Use formula (18): (A) Use formulas (13), (11), and (9): (D) B ...

(A) y′ = e−x(−2sin 2x) + cos 2x( −e−x). (C) y′ = (2 sec x)(sec x tan x). ( ...

(E) f ′(x) = 4x^3 − 12x^2 + 8 x = 4x(x − 1)(x − 2). (E) (A) (D) (E) ...

then = 4 cos t. Thus: NOTE: Since each of the limits in Questions 35–39 yields an ...

41. 42. 43. 44. 45. 46. (E) Since , f ′(0) is not defined; f ′(x) must be defined on (−8,8). (A) Note ...

(C) [We rewrite so do 3x and 4x; the fraction approaches 1 · 1 · .] (B) [We ...

(A) (D) (E) (C) (B) (f + 2 g)′(3) = f ′(3) + 2 g′(3) = 4 + 2(−1) (B) (f · g)′(2) = ...

(D) (C) (A) M′(1) = f ′(g(1)) · g′(1) = f ′(3)g′(1) = 4(−3). (B) [f(x^3 )]′ = f ...

(E) Since the water level rises more slowly as the cone fills, the rate of depth chang ...

(C) (A) Since an estimate of the answer for Question 74 is f ′(2) ≈ −5, then (B) When ...

quotient) with greater slopes than the tangent line. In both cases, f is conca ...

(B) Sketch the graph of f (x) = 1 − |x|; note that f (–1) = f ...

(E) Now (B) Note that any line determined by two points equidistant from the or ...

Use the graph of f ′(x), shown above, for Questions 98–101. (E) f ′(x) = 0 when the slope ...