Download AP Calculus AB by William Ma PDF

By William Ma

An intriguing new sequence of analysis publications that shall we each one scholar layout a process research pitched to his or her person wishes and studying style

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50 feet 10. 0 11. 21. A 1 22. 6 255 128 ln 2 89. q 77. 2π 90. 370 78. I 91. 76 81 92. 10 79. x < x2 80. 8 Answers to Diagnostic Test—Section II Part A Part B 9 1. ) 2. ) (c) f (t ) = 100 − ∫ 10 sin(πx 12)dx t 0 (d) 8 minutes 3. 5 (b) −1 (c) lim f ( x) = ∞ & lim f ( x) = 0 x →∞ x → −∞ 1 (d) − 2e (e) See solution. ) 4. (a) (b) (c) (d) (e) x=2 x=5 (−4, 0) and (4, 6) x = 0 and x = 4 See solution. 5. (a) 4 128π (b) 7 6 (c) 2 128 (d) 7 7 dy −y = dx x (b) y = 2x − 4 1 3 (c) y = − x − 2 2 (d) (2, −1) and (−2, 1) 6.

Dx (b) Write an equation of the line tangent to the graph of the equation at the point (1, −2). (c) Write an equation of the line normal to the curve at point (1, −2). 1 (d) The line y = x + 2 is tangent to the curve 2 at the point P. Find the coordinates of point P. (a) Find 5. Let R be the region enclosed by the graph of y = x3, the x-axis and the line x = 2. (a) Find the area of region R. (b) Find the volume of the solid obtained by revolving region R about the x-axis. y y=f'(x) x –4 –3 –2 –1 0 1 2 Figure D-11 3 4 5 6 0267-02/Part II 12/18/2001 17:24 Page 27 What You Need to Know About the AP Calculus AB Exam • 27 ANSWERS AND SOLUTIONS Answers to Diagnostic Test—Section I Part A 12.

G″ > 0 on (a, b). 26. When the area of a square is increasing four times as fast as the diagonals, what is the length of a side of the square? 27. The graph of f is shown in Figure D-6 on page 21 and f is twice differentiable, which of the following statements is true? y (A) f(10) < f′(10) < f ″(10) g (B) f″(10) < f′(10) < f(10) (C) f′(10) < f(10) < f ″(10) 0 a b x (D) f′(10) < f″(10) < f(10) (E) f″(10) < f(10) < f′(10) Figure D-4 19. The velocity function of a moving particle on the x-axis is given as v(t) = t2 − t.

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