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題組內容

5. (25%) The distribution of voltage on a metal plate is given by
V(x,y) = 50-x²-4y².

(c) (5%) What is the magnitude of this increase or decrease ?

其他申論題

(a) (10%) Verify that the region below the graph of f(x) = 1/x, x≥1 has infinite area.

(b) (10%) Suppose that the region (a) is revolved about the x-axis, what is the volume of the resulting solid ?

(a) (5%) At the point (1,-2), in what direction does the voltage increase most rapidly ?

(b) (5%) In what direction does the voltage decrease mostrapidly ?

(d) (10%) Describe the path of a particle that starts at the point (1,-2) and moves in the direction of greatest voltage increase.

1. 求下列各極限:(1)=________

1. 求下列各極限:(2)=________

2. 求經過曲線 3(x² + y²)² = 100xy 上點 P(3,1) 之切線方程式為何?

3. 何謂微積分基本定理(The Fundamental Theorem of Calculus)?

4. 平面上給定一點 P(0,2),試在函數 y = f(x) = 4 - x² 的圖形上找一點 Q,使 P 與 Q 兩點的距離最短_________。

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