William Ma's AP Calculus AB PDF

By William Ma

ISBN-10: 007137714X

ISBN-13: 9780071377140

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Additional info for AP Calculus AB

Example text

Given the equation y = (x + 1)(x − 3)2, what is the instantaneous rate of change of y at x = −1? 21. A function f is continuous on [−2, 0] and some of the values of f are shown below.  if x > 4 , find the lim h( x). 14. If h( x) =  2x x→4 x − x ≤ 4 12 if  15. What is the slope of the tangent to the curve y = cos (xy) at x = 0? 16. If f ′(x) = g(x) and g is a continuous function for all real values of x, then (A) ∫0 g(3x)dx is 2 1 1 f (6) − f (0) 3 3 (B) f(2) − f(0) −2 −1 0 f 4 b 4 If f(x) = 2 has no solution on [−2, 0], then b could be (A) (B) (C) (D) (E) 3 2 1 0 −2 22.

G has a point of inflection at x = −2. 79. The graph of f′, the derivative of f is shown in Figure D-7. At which value(s) of x is graph of f concave up? y 81. The velocity function of a moving particle is t3 v(t ) = − 2t 2 + 5 for 0 ≤ t ≤ 6. What is the 3 maximum acceleration of the particle on the interval 0 ≤ t ≤ 6? 82. Water is leaking from a tank at the rate of f(t) = 10 ln(t + 1) gallons per hour for 0 ≤ t ≤ 10, where t is measured in hours. How many gallons of water has leaked from the tank at exactly after 5 hours?

F' – 0 + 0 – 0 + Figure DS-17 [ [ –4 f –2 2 decr. incr. rel. min 5 decr. rel. max 6 incr. 5. See Figure DS-18 on page 38. 2 (a) Area of R = ∫ 2 0 x 3dx = rel. min Figure DS-15 Since f increases on (−2, 2) and decreases on (2, 5), f has a relative maximum at x = 2 x4  24 = −0 = 4 4  0 4 2 2 2  x7  (b) Volume of solid = π ∫ ( x 3 ) dx = π   0  7 0 = 27 ( π ) 7 = 128π 7 x 0267-02/Part II 12/18/2001 17:24 Page 38 38 • What You Need to Know About the AP Calculus AB Exam y y=x3 0 2 x x=2 Figure DS-18 a 1 ( x − 1) 2 1 1 ⇒y+2=− x+ 2 2 1  128π    2 7  (c) π ∫ ( x 3 ) dx = 0 2 Equation of normal: y − ( −2) = − a 64π πa7 64π  x7  ; ; π  = = 7 7 7 7  0 a = 64 = 2 ; a = 2 7 6 6 or y = − 7 (d) Area of cross section = ( x 3 ) = x 6 2 (d) y = −y dy 1 1 = x + 2; m = and dx x 2 2 2 Volume of solid = ∫ x7  128 x dx = = .

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AP Calculus AB by William Ma


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