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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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7. (15%) Let Ω be the region {(x, y)|(x-1)
2
+y
2
＜1}. Evaluate the double integral
其他申論題
(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
1. xsinxdx=________.
#483787
2. For the equation y3-xy2+cos(xy)=2 , at the point (0,1) is ______.
#483788
3. Let , where f iscontinuous and g and h are differentiable. Find F'(t)=___________.
#483789
4. The maximum value of f(x,y)=y2-x2 on the ellipseis=_________.
#483790
5. dydx= _________.
#483791
6.=__________.
#483792
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