1、c) d) e) 2) Give the volume of the solid generated by revolving the region bounded by the graph of y = ln(x), the x-axis, the lines x = 1 and x = e, about the y-axis.3) The graph of the derivative of f is shown below. Find the area bounded between the graph of f and the x-axis over the interval -2,1
2、, given that f(0) = 1.4) Determine dy/dt, given that and 5) The function is invertible. Give the slope of the normal line to the graph of f -1 at x = 3. 6) Determine 7) Give the polar representation for the circle of radius 2 centered at ( 0 , 2 ). 8) Determine 9) Determine 10) Give the radius of co
3、nvergence for the series 11) Determine 12) The position of a particle moving along the x-axis at time t is given by At which of the following values of t will the particle change direction? I) t = 1/8II) t = 1/6III) t = 1IV) t = 2a) I, II and IIIb) I and IIc) I, III and IVd) II, III and IVe) III and
4、 IV13) Determine 14) Determine the y-intercept of the tangent line to the curve at x = 4.15) The function f is graphed below. Give the number of values of c that satisfy the conclusion of the Mean Value Theorem for derivatives on the interval 2,5.16) Give the average value of the function on the int
5、erval 1,3.17) A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 20 square feet. Give the rate of change of the width (in ft/sec) when the height is 5 feet, if the height is decreasing at that moment at the rate of
6、 1/2 ft/sec.18) The graph of the derivative of f is shown below. Give the number of values of x in the interval -3,3 where the graph of f has inflection.19) A rectangle has its base on the x-axis and its vertices on the positive portion of the parabola What is the maximum possible area of this recta
7、ngle?20) Compute 21) Determine 22) Determine 23) Give the exact value of 24) Determine 25) Give the derivative of 26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function 27) Determine 28) Which of the following series converge(s)?a) B onlyb) A, B and Cc) B and Cd) A and Be) A and C1) d) 2) e) 3) b) 4) b) 5) e) 6) a) 7) c) 8) c) 9) b) 10) d) 11) c) 12) c) 13) c) 14) e) 15) a) 16) d) 17) a) 18) b) 19) a) 20) d) 21) b) 22) b) 23) a) 24) c) 25) d) 26) b) 27) b) 28) c)
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