Barrons AP Calculus

(A) (B) (C) (D) (D) (A) If converges, so does , where m is any positive integer; ...

45. 46. 1 − x + a 2 x^2 + a 3 x^3 + · · · = − (−1 + 2a 2 x + 3a 3 x^2 + 4a 4 x^3 + ...

1. 2. 3. 4. 5. 6. Part A (D) If f(x) = x sin for x ≠ 0 and f(0) = 0 then, thus this function ...

(C) Save time by finding the area under y = |x − 4| from a sketch! (A) Since the ...

(A) cos and thus cos x. From the equation given, y = esinx. (D) If f ( ...

For y = 2, . Note that is always negative. (B) If S represents the square of the distance ...

(A) This is of type with u = ln . (A) About the y-axis; see the figure. Washer. ...

(E) Separating variables, we get y dy = (1 − 2x) dx. Integrating gives or y^2 = 2x − ...

Thus, we must have k sin q = eq and k cos q = eq, and therefore sin q = cos q. Thus, and . The ...

(C) (A) About the x-axis. Disk. (C) (E) is a function of x alone; curves appear to ...

(C) The general solution is y = 3 ln|x^2 − 4| + C. The differential equation reveals that ...

giving . (D) Use the formula for area in polar coordinates, then the required area is given b ...

(E) Use formula (20) in the Appendix to rewrite the integral as (E) The area, A, is repre ...

So, if , then . (C) The speed, |v|, equals , and since x = 3y − y^2 , Then |v| is ...

...

58. 59. 60. 61. 62. 63. Part B (D) Since h is increasing, h′ ≥ 0. The graph of h is concave downward for x ...

We see that f ′ and f ′′ are both positive only if x > 1. (E) Note from t ...

(D) Note that f(g(u)) = tan−^1 (e^2 u); then the derivative is . (D) Let . Then cos (xy)[xy′ + ...

(C) About the x-axis; see the figure. Washer. (C) By the Mean Value Theorem, there is a number c ...

Use disks; then ΔV = πR^2 H = π(arc sec y)^2 Δy. Using the calculator, we find that (C) If Q ...