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研究所、轉學考(插大)-微積分
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105年 - 105 國立臺灣大學轉學生招生考試試題_(商、管、農、經學院聯招) ：微積分(C)#113221
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3. (10%) Compute the indefinite integral
=_____
其他申論題
(a) (5%) The value g(1) must be 2. True or false? Answer:_____
#483776
(b) (10%) The derivative g'(1)=_____
#483777
(a) (5%) Let s(t) be the distance (in meters) between the two particles in t minutes. s(t)=_____
#483778
(b) (10%) Suppose at t= t0 the two particles are closest to each other. Then t0=_____
#483779
4. (10%) Let Ω be a regioin (on the xy-plane) enclosed by , x=0 and y=e. Let S be the solid obtained by revolving Ω about the y-axis. Let V be the volume of S. V=_____
#483781
(a) (10%) If the unit vector u (in the xy-plane) at p is the direction (among all directions at p) along which the height (i.e. the value of z) of S increases most rapidly, then u =_____
#483782
(b) (10%) Write H for the plane x+2y+3z=1 and the curve C for the intersection S∩H. Let L be the tangent line to C at P and N be the plane perpendicular to L at P. Then the equation of N is _____
#483783
(a) (10%) Let A be the area of R. A=_____
#483784
(b) (5%) The double integral =_____
#483785
7. (15%) Let Ω be the region {(x, y)|(x-1)2+y2＜1}. Evaluate the double integral
#483786
=_____
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=_____