Barrons AP Calculus - David Bock
19. (B) ...
20. (C) ...
(D) Let y ′ be then 3x^2 − 3y^2 y ′ = 0; ...
(A) 1 − sin (x + y)(1 + y ′) = 0; ...
(D) cos x + sin y · y′ = 0; ...
(B) 6 x − 2(xy ′ + y) + 10yy ′ = 0; y ′(10y − 2x) = 2y − 6x. ...
25. (A) ...
(E) f ′(x) = 4x^3 − 12x^2 + 8x = 4x(x − 1)(x − 2). ...
(E) f ′(x) = 8x−1/2; ...
(A) f (x) = 3 ln x; Replace x by 3. ...
(D) 2 x + 2yy ′ = 0; ...
(E) Replace t by 1. ...
31. (D) ...
(D) y ′ = ex · 1 + ex (x − 1) = xex; y ′′ = xex + ex and y ′′(0) = 0 · 1 + 1 = 1. ...
(E) When simplified, ...
(B) Since (if sin t ≠ 0) = −2 sin t = −4 sin t cos t and then Thus: BC ONLY ...
NOTE: Since each of the limits in Questions 35–39 yields an indeterminate form of the type we can apply L’Hôpital’s Rule in each ...
(B) The given limit is the definition for f ′(8), where f (x) = ...
(B) The given limit is f ′(e), where f (x) = ln x. ...
(B) The given limit is the derivative of f (x) = cos x at x = 0; f ′(x) = − sin x. ...
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