Section I,Part A,不可使用任何計(jì)算器: 6)The slope of the line tangent to the graph of y=ln(1-x) at x = -1 is
(A)1-
(B)-1/2
(C)1/2
(D)ln2
(E) 1
7)Let y = f(x) be the solution to the differential equation dy/dx = f'(x) with initial condition f(x)=3. Selected values of f' are given in the table above. What is the approximation for f(2.4) if Euler’s method is used, starting at x=2 with two steps of equal size?
2.80
2.82
2.84
2.92
3.16
11)The function f is continuous on the closed interval [0,6] and has values as shown in the table above. Using the intervals [0,2],[2,4] and [4,6], what is the approximation of obtained from a midpoint Riemann sum?
0
3
4
6
8
14)The figure above shows the graph of a function f. Which of the following could be the second-degree Taylor polynomial for f about x=2?
2-x-x2
2+x-x2
2-(x-2)+(x-2)2
2+(x-2)-(x-2)2
2+(x-2)+(x-2)2
Section II,Part B,請(qǐng)使用Graphing Calculator: 76)A music group expects to sell a new compact disc (CD) at the rate R(t) = 20,000e-0.12t CDs per week, where t denotes the number of weeks since the CD was first released. To the nearest thousand, how many CDs are expected to be sold during the first 12 weeks after the release?
5,000
11,000
57,000
127,000
240,000
77)Let f be a function that is continuous on the closed interval[1,3] with f(1)=10 and f(3) =18. Which of the following statements must be true?
10≤f (2)≤18
f is increasing on the interval [1,3]
f(x)=17has at least one solution in the interval [1,3]
f'(x)=8has at least one solution in the interval (1,3)
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