Barrons AP Calculus - David Bock
(C) We partition [0, 2] into n equal subintervals each of time Δt hr. Since the 18-wheeler gets (4 + 0.01v) mi/gal of diesel, i ...
Answers Explained (C) v(t) = 2t^2 − t + C; v(1) = 3; so C = 2. ...
(B) If a(t) = 20t^3 − 6t, then v(t) = 5t^4 − 3t^2 + C 1 , s(t) = t^5 − t^3 + C 1 t + C 2 , Since s(−1) = −1 + 1 − C 1 + C 2 = 2 ...
(D) From Answer 2, s(t) = t^5 − t^3 + t + 3, so s(0) = C 2 = 3. ...
(B) Since a(t) = −32, v(t) = −32t + 40, and the height of the stone s(t) = −16t^2 + 40t + C. When the stone hits the ground, 4 ...
(C) From Answer 4 s(t) = −16t^2 + 40t + 96. Then s ′(t) = −32t + 40, which is zero if t = 5/4, and that yields maximum height, ...
(E) The velocity v(t) of the car is linear, since its acceleration is constant and ...
(B) Since v = 100 − 20t, s = 100t − 10t^2 + C with s(0) = 0. So s(1) = 100 − 10 = 90 ft. ...
8. (A) ...
(A) The odometer measures the total trip distance from time t = a to t = b (whether the car moves forward or backward or revers ...
(E) (A), (B), (C), and (D) are all true. (E) is false: see Answer 9. ...
(A) Integrating yields + C or y^2 = x^2 + 2C or y^2 = x^2 + C ′, where we have replaced the arbitrary constant 2C by C ′. ...
(C) For initial point (−2,1), x^2 − y^2 = 3. Rewriting the d.e. y dy = x dx as reveals that the derivative does not exist when ...
(E) We separate variables. The initial point yields ln hence c = −2. With y > 0, the particular solution is ln ...
(C) We separate variables. The particular solution is −e−y = x − 2. ...
(B) The general solution is when x = 4 yields C = 0. ...
(E) Since it follows that ln y = ln x + C or ln y = ln x + ln k; so y = kx. ...
(E) hence the general solution is y = kex, k ≠ 0. ...
(A) We rewrite and separate variables, getting The general solution is ...
(C) We are given that The general solution is ln |y| = 3 ln |x| + C. Thus, |y| = c |x^3 |; y = ±c x^3. Since y = 1 when x = 1, ...
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