Associate Press. Sports Writing Handbook by Wilstein S

By Wilstein S

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As x Æ 0ϩ, this l/x function has the indeterminate form ϱ/ϱ. Apply L’Hôpital’s rule: lim+ ln y = lim+ x→0 x→0 1/ x −1 / x 2 = lim+ ( − x ) = 0. x→0 0 So y Æ e or 1. 12. (A) Use the Parts Formula with u = x and dv = ex dx. Then du = dx and v = ex, and ( xe 15. (B) x − ∫ e x dx ) = ( xe 1 0 x − ex The arc length is given by the integral Ύ 1 0 ) 1 0 = ( e − e ) − ( 0 − 1) . 1 + ( 3 x ) dx which is 1 2 1 1 1/ 2 3/ 2 1 + 9 x ) ( 9dx ) = i (1 + 9 x ) ( ∫ 9 3 9 0 16. (E) Separating variables yields 1 2 2 1 0 = ( ) 2 103 / 2 − 1 .

40. 547 . a 2 0 (D) If x = 2t ϩ 1, then t = x − 1 , so dt = 1 dx . When t = 0, x = 1; when t = 3, x = 7. 2 2 (E) Use A(t) = A0ekt, where the initial amount A0 is 50. Then A(t) = 50ekt. Since . 9 . 3 . 9 t 35 Diagnostic Test Calculus AB 7_4324_APCalc_01DiagnosticAB Diagnostic Test Calculus AB 7_3679_APCalc_01DiagnosticAB 36 10/3/08 4:18 PM Page 36 AP Calculus 26 y x 41. (C) See the figure above. Since x2 ϩ y2 = 262, it follows that dy 2 x dx + 2 y = 0 dt dt at any time t. When x = 10, then y = 24 and it is given that Hence, 2(10)(3) + 2(24) 42.

6 Note that the distance covered in 6 seconds is 6 ∫0 v(t ) dt , the area between the velocity curve and the t-axis. −2 − 0 . 5− 4 21. (C) Acceleration is the slope of the velocity curve, 22. (D) Particular solutions appear to be branches of hyperbolas. See page 21. 23. (A) Differentiating implicitly yields 2xyyЈ + y2 – 2yЈ + 12y2yЈ = 0. When y = 1, x = 4. Substitute to find yЈ. 24. (C) 25. (D) 26. (B) Separate to get x ∫a g(t ) dt − x ∫b g(t ) dt dy y 2 = x ∫a g(t ) dt = 2 x dx , − + b ∫x g(t ) dt = b ∫a g(t ) dt.

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