AP微積分BC選擇題Section2練習(xí)

1、.29) find the average value of the function over the interval 0, 4.a) b) c) d) e) 30) what is the y-intercept of the line tangent to the curve y = x2 + 7 at x = 3?a) b) c) d) e) 31) which of the following function(s) is continuous and differentiable?i. ii. iii. a) i and iii onlyb) iii onlyc) i and i

2、i onlyd) i onlye) ii only32) find m a) b) c) d) e) 33) the graph of the derivative of f is shown below. which of the following must be true?a) f is concave down on 0, 4.b) f is increasing on -2, 2.c) f has a local maximum at x = 0.d) f has a local minimum at x = -2.e) f has a point of inflection at

3、x = 4.34) the sum of two positive integers x and y is 60. find the value of x that minimizes a) b) c) d) e) 35) a particle moves on the curve find the speed of the particle at time t = .a) 7.1414b) 6.7082c) 7.2801d) 3.3166e) 3.000036) the function f is defined as x 6which of the following is false?a

4、) f has a horizontal asymptote at y = 1.b) f has a vertical asymptote at x = 6.c) f is decreasing on 3, 6.d) f has a local maximum at x = 3.e) f is concave up for x > 6.37) a particle is moving along the x-axis and its position at time t > 0 is given by which of the following is (are) true?i.

5、the particle changes direction at x = 2 and x = 6.ii. the particle is slowing down on 0, 2.iii. the particle is speeding up on 2, 6.a) ii and iii onlyb) i onlyc) ii onlyd) i and iii onlye) i, ii and iii38) f (x) is a differentiable function and it is decreasing on (,).if then g has a local maximum a

6、ta) b) c) d) e) 39) the rate at which a bacteria population grows is proportional to the number of bacteria present. initially, there were 1000 bacteria present and the population doubled in 5 hours. roughly how many hours does it take for the population to reach 10000?a) b) c) d) e) 40) find the ra

7、dius of convergence of the series a) b) c) d) e) 41) for 0 < x < 3the graph of g is shown above. which of the following must be true?i. ii. iii. a) ii and iii onlyb) ii onlyc) i and iii onlyd) i and ii onlye) i only42) if the region bounded by y = tan-1(x), y = and the y-axis is rotated about

8、the y-axis, the volume of the solid formed isa) 0.674b) 0.215c) 1.348d) 0.430e) 0.41343) f (x) is represented by the maclaurin serieswhat is the slope of the line normal to the graph of f at x =?a) b) c) d) e) 44) what are all values of h for which converge?a) h > 1b) h < 1c) h > 1d) h < 1e) -1 < h < 145) the base of a solid is the region bounded by the x-axis, andthe line x = 7each cross-section of the solid perpendicular to the x-axis is a square, with one side on the xy-plane. which of the follo