Calculus Lessons & Past Papers
Part A, Q1 - 28
Part B, Q76 - 92
28. What is the coefficient of x2 in the Taylor series for
76. The graph of the function f is shown above. Which of the following statements must be false?
77. Let P(x)
78. The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20π meters?
79. The table above gives values of
80. Insects destroyed a crop at the rate of
81. The graph of the function f is shown in the figure above.
82. The rate of change of the altitude of a hot-air balloon is given by
83. The function f is continuous and differentiable on the closed interval [0,4]. The table above gives selected values of f on this interval. Which of the following statements must be true?
84. A particle moves in the xy-plane so that its position at any time t is given by
85. If a trapezoidal sum overapproximates
86. Let f be the function with derivative defined by
87. A particle moves along the x-axis so that at any time t ≥ 0, its velocity is given by v(t) = cos(2 - t2) The position of the particle is 3 at time t = 0. What is the position of the particle when its velocity is first equal to 0?
88. On the closed interval [2,4], which of the following could be the graph of a function f with the property that
89. The region bounded by the graph of y = 2x - x2 and the x-axis is the base of a solid. For this solid, each cross-section perpendicular to the x-axis is an equilateral triangle. What is the volume of this solid?
90. The graph of f ‘, the derivative of the function f , is shown above. If f (0) = 0, which of the following must be true?
91. The height h, in meters, of an object at time t is given by
92. Let f be the function defined by f(x) = x + ln x. What is the value of c for which the instantaneous rate of change of f at x = c is the same as the average rate of change of f over [1,4] ?
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