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題組內容

4. (20%)

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

其他申論題

2. (15%) Show that ln(1+x) ≈ x as x→0. (Hint: (ln(x))'=1/x)

(a) (10%) Find the critical numbers of F and determine theintervals on which F is increasing and the intervals onwhich F is decreasing.

(b) (10%) Determine the concavity of the graph of F and find thepoints of inflection (if any).

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

(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 ?

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

(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)=________

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