By Shirley O. Hockett, David Bock
Either Calculus AB and Calculus BC are lined during this accomplished AP try education handbook. potential attempt takers will locate 4 perform tests in Calculus AB and 4 extra in Calculus BC, with all questions responded and ideas defined. The handbook additionally offers a close 10-chapter assessment overlaying themes for either checks. The authors additionally provide an summary of the AP Calculus tests, together with recommendation to scholars on making most sensible use in their graphing calculators.
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B) Since |x Ϫ 2| = 2 Ϫ x if x Ͻ 2, the limit as x Æ 2Ϫ is 20. (A) Average speed = 20. A. 2− x = −1. x−2 distance covered in 6 sec time elapsed 1 1 π(4 2 ) + (1 ⋅ 2) + 1 ⋅ 2 2 The average sp = 4 . 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.
Multiple-Choice Part A 7. (D) ∞ The volume is given by π ∫ e −2 x dx , an improper integral. 0 k⎞ ⎛ 1 = lim ⎜ − πe −2 x ⎟ x →∞ ⎝ 2 0⎠ ( ( 1 = lim − π e −2 k − e 0 2 k →∞ π = 2 9. (B) Let y = xx and take logarithms. ln y = x ln x = )) ln x . 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.
Equation x 2 e y dx (a) Solve the differential equation, expressing y as a function of x and specifying the domain of the function. (b) Find the equation of each horizontal asymptote to the graph of y = f(x). 6. The graph of function f consists of the semicircle and line segment shown in the figure. Define the area function A( x ) = 6 0 Ύ x f (t ) dt for 0 ≤ x ≤ 18. 0 (18,6) f 6 12 18 (a) Find A(6) and A(18). (b) What is the average value of f on the interval 0 ≤ x ≤ 18? (c) Write the equation of the line tangent to the graph of A at x = 6.
AP Calculus by Shirley O. Hockett, David Bock