所屬科目：研究所、轉學考(插大)-微積分
(a) ；
(b)；
(c) (sin x)x；
(d) ；
(e).(20 分)
3.Find the tangential and normal components of acceleration for the position vector given by . (12 分)
(a)cos nxcosmxdx，
5.Evaluate the following double integral over the square R in Fig. 1. (10 分) (x² + y²) dxdy
(a)C₁: the straight-line segment , 0 ≤ t ≤ 1. (8 分)
(b)C₂: the parabolic arc , 0 ≤ t ≤ 1. (8 分)
(a)Show that vector = (2xyz²)+ (x²z² + zcos(yz) + (2x²yz + ycos(yz) is a conservative field. (7 分)
(b)Find the scalar potential function for . (8 分)
(c)Evaluate the work done in moving an object in this field from A:(0, 0, 1) to B:(1, ,2). (5 分)
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；
；
(sin x)x；
；
.(20 分)
. (12 分)
cos nxcosmxdx，
(x² + y²) dxdy
, 0 ≤ t ≤ 1. (8 分)
, 0 ≤ t ≤ 1. (8 分) 
= (2xyz²)
+ (x²z² + zcos(yz)
+ (2x²yz + ycos(yz)
is a conservative field. (7 分)
. (8 分)
,2). (5 分)