Single Variable Calculus_西北工业大学中国大学mooc课后章节答案期末考试题库2023年
1.If f (x) and g (x) are differentiable on (a, b), 【图片】and f (x) > 0, g (x) > 0, x∈(a, b), then when x∈(a, b), we have

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2.For what values of a and b will 【图片】be differentiable for all values of x?

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a=-1/2, b=1

3.The evaluation of integral【图片】(where x>1) is


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variable used in lambda
4.Find the derivative of【图片】

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5.Find the centroid of a thin, flat plate covering the “triangular” region in the first quadrant bounded by they-axis, the parabola【图片】, and the line【图片】.

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6.If【图片】, find the limit of g(x) as x approaches the indicated value.

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7.Find the derivative of the function below at x=0,【图片】

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8.【图片】is

答案:
-1/32

9.If f (x) is continuous and F′(x) = f(x), then

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10.Find the volume of the solid generated by revolving the region bounded by the curve【图片】and the lines【图片】about【图片】.

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11.The mean value【图片】that satisfies the Rolle’s Theorem on the function【图片】is

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12.The critical number of 【图片】is ( )

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0 and 2

13.Which statement is true?【图片】

答案:
A

14.If【图片】,then【图片】

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15.Evaluate【图片】.

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16.The integtral of【图片】is

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17.When x approaches infinity, the limit of【图片】is

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18.The evaluation of integral【图片】is

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19.If【图片】has continuous second-order derivative, and【图片】, then

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20.Find the length of the enclosed loop【图片】shown here. The loop starts at【图片】and ends at【图片】.【图片】

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21.The height of a body moving vertically is given by 【图片】, with s in meters and t in seconds. The body’s maximum height is ( )

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22.If f (x) is increasing and f(x) > 0, then

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23.A rock climber is about to haul up 100 N of equipment that has been hanging beneath her on 40 m of rope that weighs 0.8 newton per meter. How much work will it take? (Hint: Solve for the rope and equipment separately, then add.)

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24.The integral of【图片】is

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