北语网院18春《高等数学（下）》作业_1（100分)

北京语言大学18春《高等数学（下）》作业_1
试卷总分:100    得分:100

第1题,二重积分_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image414.gif" width="80" height="39"/>}（   ），D为_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image412.gif" width="167" height="21"/>}所围成的矩形区域。
A、<span>0</span>
B、<span>1             </span>
C、<span>-1  </span>
D、<span>2</span>

第2题,<img src="http://otsstatic.chinaedu.net/ots/blcu/eblcuimage/3742.BMP"/>
A、[A]
B、[B]
C、[C]
D、[D]www.youxue100f.com

第3题,_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image034.gif" width="95" height="24"/>}的通解为（   ）
A、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image036.gif" width="76" height="21" />}</span>
B、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image038.gif" width="88" height="21" />}              </span>
C、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image040.gif" width="96" height="21" />}  </span>
D、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image042.gif" width="96" height="21" />}</span>

第4题,设_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image266.gif" width="117" height="24"/>}，则_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image268.gif" width="49" height="47"/>}（   ）
A、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image270.gif" width="13" height="19" />}</span>
B、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image272.gif" width="12" height="19" />}            </span>
C、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image274.gif" width="21" height="19" />} </span>
D、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image098.gif" width="13" height="17" />}</span>

第5题,<img src="http://otsstatic.chinaedu.net/ots/blcu/eblcuimage/3773.jpg"/>
A、[A]
B、[B]
C、[C]
D、[D]

第6题,<img src="http://otsstatic.chinaedu.net/ots/blcu/eblcuimage/3727.GIF"/>
A、[A]
B、[B]
C、[C]
D、[D]

第7题,设_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image158.gif" width="159" height="24"/>}则_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image160.gif" width="61" height="24"/>}（   ）
A、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image094.gif" width="9" height="17" />}</span>
B、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image096.gif" width="21" height="17" />}                  </span>
C、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image098.gif" width="13" height="17" />}  </span>
D、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image100.gif" width="25" height="17" />}</span>

第8题,若_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image330.gif" width="45" height="24"/>}，则_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image332.gif" width="55" height="48"/>}（   ）
A、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image334.gif" width="12" height="15" />}</span>
B、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image327.gif" width="16" height="13" />}                    </span>
C、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image325.gif" width="16" height="41" />}  </span>
D、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image338.gif" width="28" height="41" />}</span>

第9题,级数_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image496.gif" width="77" height="47"/>}的收敛域为（   ）
A、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image498.gif" width="36" height="21" />}</span>
B、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image500.gif" width="37" height="21" />}             </span>
C、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image502.gif" width="37" height="21" />}  </span>
D、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image504.gif" width="36" height="21" />}</span>

第10题,函数_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image074.gif" width="103" height="21"/>}的全微分为（   ）
A、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image076.gif" width="251" height="23" />}</span>
B、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image078.gif" width="206" height="24" />}            </span>
C、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image080.gif" width="367" height="24" />}  </span>
D、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image082.gif" width="165" height="22" />}</span>

第11题,如果_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image311.gif" width="52" height="21"/>}具有二阶连续偏导数，则_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image313.gif" width="83" height="47"/>}（   ）
A、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image315.gif" width="69" height="44" />}</span>
B、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image317.gif" width="69" height="44" />}           </span>
C、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image319.gif" width="69" height="47" />}  </span>
D、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image321.gif" width="69" height="47" />}</span>

第12题,两个非零矢量<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image055.gif" width="13" height="19"/>与<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image056.gif" width="15" height="23"/>相互垂直的充要条件是（   ）
A、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image058.gif" width="57" height="19" />}</span>
B、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image060.gif" width="53" height="19" />}                 </span>
C、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image062.gif" width="49" height="19" />}  </span>
D、<span>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image064.gif" width="54" height="19" />}</span>

第13题,<img src="http://otsstatic.chinaedu.net/ots/blcu/eblcuimage/3770.GIF"/>
A、[A]
B、[B]
C、[C]
D、[D]

第14题,<img src="http://otsstatic.chinaedu.net/ots/blcu/eblcuimage/3733.jpg"/>
A、[A]
B、[B]
C、[C]
D、[D]

第15题,_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image416.gif" width="53" height="27"/>}在平面闭区域D上有界是二重积分_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image418.gif" width="101" height="39"/>}存在的（   ）
A、<span>必要条件</span>
B、<span>充分条件              </span>
C、<span>充要条件  </span>
D、<span>无关条件</span>

第16题,若级数_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image646.gif" width="40" height="45"/>}收敛，则_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image648.gif" width="75" height="29"/>}。
√、对
×、错
正确答案:√

第17题,设_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image580.gif" width="85" height="24"/>}，则_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image582.gif" width="83" height="44"/>}。
√、对
×、错
正确答案:×

第18题,函数_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image668.gif" width="181" height="24"/>}有极小值。
√、对
×、错
正确答案:×

第19题,函数<em>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image723.gif" width="92" height="24"/>}</em>的全微分<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image725.gif" width="33" height="19"/><i>-</i>_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image727.gif" width="108" height="24"/>}。
√、对
×、错
正确答案:×

第20题,设_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image693.gif" width="77" height="21"/>}，则一定有_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image715.gif" width="88" height="47"/>}成立。
√、对
×、错
正确答案:×

第21题,设_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image378.gif" width="75" height="21"/>}在点_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image657.gif" width="51" height="24"/>}处可微，则_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image378.gif" width="75" height="21"/>}在点_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image657.gif" width="51" height="24"/>}必定连续。
√、对
×、错
正确答案:√

第22题,设函数_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image104.gif" width="51" height="21"/>}在点_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image641.gif" width="53" height="24"/>}处的偏导数_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image643.gif" width="49" height="44"/>}都存在，则_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image104.gif" width="51" height="21"/>}在该点处可微。
√、对
×、错
正确答案:×

第23题,_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image705.gif" width="57" height="24"/>}在点_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image264.gif" width="32" height="21"/>}处，当_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image708.gif" width="65" height="19"/>}，_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image710.gif" width="73" height="21"/>}时的全微分是_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image712.gif" width="33" height="19"/>}。
√、对
×、错
正确答案:√

第24题,常微分方程都是一阶的。
√、对
×、错
正确答案:×

第25题,若函数_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image584.gif" width="76" height="21"/>}在_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image586.gif" width="64" height="24"/>}处的两个偏导数_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image600.gif" width="69" height="24"/>}与_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image602.gif" width="65" height="25"/>}均存在，则该函数在_{<img src="http://otsstatic.chinaedu.net/ots/blcu/quesimages/e0/25/52ae8b22-7d74-4fb3-af06-81b3837ce025/xia.files/image164.gif" width="16" height="17"/>}点处一定连续。
√、对
×、错
正确答案:×