By William Ma
An interesting new sequence of analysis publications that we could every one scholar layout a process examine pitched to his or her person wishes and studying style
Each 12 months, multiple million U.S. highschool scholars take a number of complex placement (AP) checks, and, in response to professional projections, that quantity will proceed to upward push within the years forward. that's simply because AP tests confer very important merits on those that do good on them. excessive AP rankings are fundamental to gaining admission to such a lot elite schools. they supply scholars with a aggressive part while competing for supplies and scholarships. and so they permit scholars to circumvent required collage survey classes, saving on skyrocketing college fees.
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Additional info for AP Calculus AB
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 = = .
AP Calculus AB by William Ma