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111 年 - 111 國立臺灣大學轉學生招生考試試題_理工科聯招:微積分(B)#110846 

選擇:0題,非選:20題 我要補題 回報試卷錯誤
【非選題】
1.

1.


【題組】(a)6328019a7bf42.jpg=__(1)__



【非選題】
2.【題組】

(b)632801bfa9cde.jpg=__(2)__



【非選題】
3.【題組】

(c)632801ebe9422.jpg=__(3)__



【非選題】
4.
2.

【題組】

(a) Let f(x,y)=6328028140eff.jpg=__(4)__。



【非選題】
5.【題組】

(b) Let g(x) = 632802b293eff.jpg =__ (5)__



【非選題】
6.

3. Consider a function f : (-π,π)→R deined by
632802e4a4400.jpgIf f is differentiable on (-π,π), then (a, b) = __(6)__



【非選題】
7.4. Consider the paramettic curvex = 2t2 + 1, y= 4t. Let P be the point (2p2 + 1,4P). The greatest value of p such that the normal to the curve at P passes through (31, -24) is p =__ (7)__

【非選題】
8.

5. Let f(x,y,z)= 6328037151ed4.jpgdt. The linearization of f(x,y,z) at (1.1,0) is L(x,y,z)=__(8)__



【非選題】
9.
6.

【題組】

(a) 632803b17fdf7.jpgdo=__(9)__



【非選題】
10.【題組】

(b) Let D be the region enclosed by the curve y =632803dabdaef.jpg and the x-axis. The volume of the solid obtained by revolving D about the x-axis is (10)



【非選題】
11.7. Let f(x, u) = 2x3 - 12xy +y3 +13. Let P= (p,q) be the point on R2 at which the rate of change of f(x,y) in the direction it j is the smallest. Then (p,q) =__ (11)__

【非選題】
12.
8.

【題組】

(a)632804730e522.jpgdydx=_________



【非選題】
13.【題組】

(b) Let R={(x,y)632804a3e59c1.jpg= __(13)__



【非選題】
14.
9.

【題組】

(a) The work done by the force feld F(x, y) = 632804e14af57.jpg j in moving a particle along a triangular path with vertices (0,0), (1,0), (2,2) counter-clockwisely is__ (14)__



【非選題】
15.【題組】

(b) Let S be part of the cone z = 6328052c8376c.jpg that lies bellow the plane :x + z = 1. Then 632805557b552.jpgxdS=__(15)__



【非選題】
16.【題組】

(c) Let D be a closed surface in R3, oriented outward. The maximum Aux of the vector field 632805ae047b9.jpgamong all possible choices of D is __(16)__.



【非選題】
17.

10. The greatest value of p such that the series632805f725fa9.jpg converges conditionally is p=__(17)__.



【非選題】
18.

1. Consider the function f:R2→ R defined by 632806941ad93.jpg


【題組】 (a) Is f continuous at (0,0)? Justify your answer.


【非選題】
19.【題組】(b) Let u = ai+ bj be a unit vector. Find the directional derivative of f at (0,0) in the direction u. Express your answer in terms of a and b.

【非選題】
20.【題組】(c) Find the direction(s) that f changes the most rapidly at (0,0).

懸賞詳解

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111 年 - 111 國立臺灣大學轉學生招生考試試題_理工科聯招:微積分(B)#110846-阿摩線上測驗

111 年 - 111 國立臺灣大學轉學生招生考試試題_理工科聯招:微積分(B)#110846