2026軍隊(duì)文職數(shù)學(xué)1筆試跟練6

1. 設(shè)函數(shù)，則在點(diǎn)處的值為（   ）.

A.                                                       B.

C.                                                       D.

2. 曲線方程,則在處法平面方程為（   ）.

A.                                    B.

C.                                    D.

3. 設(shè),則在點(diǎn)處（   ）.

A. 連續(xù)但偏導(dǎo)不存在                             B. 偏導(dǎo)存在但不連續(xù)  

C. 不可微                                               D. 偏導(dǎo)數(shù)連續(xù)

4. 設(shè)，其中

，則（   ）.

A.                                          B.

C.                                           D.

5. 由四個(gè)平面所圍成的柱體被平面截得的立體的體積是（   ）.

A.                                                       B. 1

C.                                                       D.

1.答案：B.解析：本題考查二元函數(shù)的混合偏導(dǎo)數(shù).

，，

于是.（先對(duì)求偏導(dǎo)后代入值，再對(duì)求偏導(dǎo)代入值更節(jié)約時(shí)間）.

2.答案：C.解析：本題考查曲線的法平面.

，

故法向量為，

故法平面為，即.

3.答案：C.解析：本題考查多元函數(shù)的可微性.

因?yàn)?img height="30" src="data:image/wmf;base64,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" width="126" />，所以，故在點(diǎn)處連續(xù)..

因?yàn)?img height="54" src="data:image/wmf;base64,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" width="426" />，

所以在點(diǎn)處不可微.

4.答案：B.解析：本題考查比較二重積分的大小.

由于當(dāng)時(shí)，為減函數(shù)，此時(shí)，于是，故.

5.答案：C.解析：本題考查二重積分.

.

技巧：對(duì)稱性更節(jié)約時(shí)間.

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