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103 台聯大微積分(A2) 第 8 題

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103學年度 · 103微積分A2 · 第 8 題

題目

Problem

甲、填充題:共 10 題,每題 8 分,共 80 分。請將答案依題號順序寫在答案卷上,不必寫演算過程。

  1. Suppose that the edge lengths xx, yy, and zz of a rectangular box are changing at the following rates: dxdt=1\dfrac{dx}{dt}=1 m/sec, dydt=2\dfrac{dy}{dt}=-2 m/sec, dzdt=1\dfrac{dz}{dt}=1 m/sec. Find the rate at which the box’s volume is changing at instant when x=4x=4, y=3y=3, and z=2z=2. Answer : \underline{\quad(1)\quad}

解答