Barrons AP Calculus - David Bock
From the equations for x and y, dx = (1 − cos θ) dθ and dy = sin θ dθ. (a) The slope at any point is given by which here is Whe ...
Both curves are circles with centers at, respectively, (2,0) and the circles intersect at The common area is given by The answ ...
(a) For f (x) = cos x, f′ (x) = −sin x, f ′′ (x) = −cos x, f ′′′(x) = sin x, f(4) (x) = cos x, f(5) (x) = −sin x, f(6) (x) = −c ...
(a) Since y = 2t + 1 and x = 4t^3 + 6t + 3t. (b) Since then, when t = 1, |a| = 36. ...
See the figure. The required area A is twice the sum of the following areas: that of the limaçon from 0 to and that of the circ ...
Answers Explained Multiple-Choice Part A (C) Use the Rational Function Theorem. ...
(C) Note that where f (x) = ln x. ...
(B) Since y ′ = −2xe−x^2 , therefore y ′′ = −2(x · e −x^2 · (−2x) + e −x^2 ). Replace x by 0. ...
4. (B) ...
(B) h ′(3) = g ′(f (3)) · f ′(3) = g ′(4) · ...
(E) Since f ′(x) exists for all x, it must equal 0 for any x 0 for which f is a relative maximum, and it must also change sign ...
(E) By the Quotient Rule (formula (6)), ...
(A) Here, f ′(x) is e −x (1 − x); f has maximum value when x = 1. ...
(A) Note that (1) on a horizontal line the slope segments are all parallel, so the slopes there are all the same and must depen ...
(E) Acceleration is the derivative (the slope) of velocity v; v is largest on 8 < t < 9. ...
(C) Velocity v is the derivative of position; because v > 0 until t = 6 and v < 0 thereafter, the position increases unti ...
(D) From t = 5 to t = 8, the displacement (the integral of velocity) can be found by evaluating definite integrals based on the ...
(A) The integral is of the form evaluate ...
14. (E) ...
15. (D) ...
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