大学高等数学测试题

大学高等数学测试 Quiz Chinese Name: Class: Date: 2017-2 A. Translation B. Please solve the problems in English. 1. Find the equation of the to the curve . . 3. Differentiate each of these functions f(x). Give your answers f’(x) in a similar form, without negative or fractional indices(负指数或分数指数). (a) (b) (c) (d) (e) (f) 4. Given the function , find (a) f’(-2) (b) the values of a such that f’(a)=56. 5. Find the coordinates of the stationary points on the graphs of the function , and find whether theses points are maxima or minima. 6. Differentiate the following with respect to x. (a) (b) (c) (d) Additional paper(附加题): 7. The of two x and y is 12. Find the 8. The volume of a cylinder(圆柱体) is given by the formula(公式) . Find the greatest and least values of V if r+h=6. 9. Use differentiation to find the coordinates of the stationary points on the curve and determine whether each stationary point is a maximum or a minimum point. Find the set of values of x for which y increases as x increases. 10. Air is being lost from a spherical balloon(圆形的气球) at a constant rate of 0.6m3s-1. Find the rate at which the is decreasing at the instant(在那个瞬间) when the radius is 2.5m.