1. 函數(shù)
與
和坐標(biāo)軸所圍成圖形面積是（ ）.
A. 
B. 
C. 
D. 
2. 二次曲面中，代表橢圓拋物面的方程是（ ）.
A. 
B. 
C. 
D. 
3. 過(guò)直線
且垂直于平面
的平面方程是（ ）.
A. 
B. 
C. 
D. 
4. 已知
（
）為某二元函數(shù)的全微分，則常數(shù)
需滿足（ ）.
A. 
B. 
C. 
D. 
5. 設(shè)
與
均為可微函數(shù)，且
.已知
是在約束條件
下的一個(gè)極值點(diǎn)，下列選項(xiàng)正確的是（ ）.
A. 若
，則
B. 若，則 
C. 若
，則
D. 若，則
1.答案：B.解析：本題考查函數(shù)的定積分的應(yīng)用.
所圍面積都是正數(shù)，不存在奇函數(shù)在對(duì)稱區(qū)域積分為零.
故
.
2.答案：C.解析：本題考查二次曲面標(biāo)準(zhǔn)方程.
A代表橢球面，B代表雙葉雙曲面，D代表二次錐面，故選C.
3.答案：B.解析：本題考查平面的方程.
直線L的方向向量為
，平面
的法向量
，所求平面法向量
.平面過(guò)直線上的點(diǎn)
，由平面方程的點(diǎn)法式得
，即.
4.答案：B.解析：本題考查全微分方程的等價(jià)條件.
設(shè)
.
為某二元函數(shù)的全微分
.因?yàn)?img height="42" src="data:image/wmf;base64,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" width="225" />，
，所以
，即，故選B.
5.答案：D.解析:本題考查多元函數(shù)微分學(xué)的應(yīng)用.
設(shè)
由已知，點(diǎn)
是
在約束條件下的極值點(diǎn)，故有
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