第六届全国大学生数学竞赛非数学类试题.docVIP

2014年全国大学生数学竞赛预赛试题 非数学类 填空题(共有5小题，每题6分，共30分) 已知和是齐次二阶常系数线性微分方程的解，则该方程是___ _________________________________ 设有曲面和平面。则与平行的的切平面方程是_______________________________ 设函数由方程所确定。求_______________ 设。则______________________ 已知。则____________________ （本题12分）设为正整数，计算。 （本题14分）设函数在上有二阶导数，且有正常数使得。证明：对任意，有。 （本题14分）（1）设一球缺高为，所在球半径为。证明该球缺体积为。球冠面积为；（2）设球体被平面所截得小球缺为，记球冠为，方向指向球外。求第二型曲面积分 （本题15分）设在上非负连续，严格单增，且存在，使得。求 （本题15分）设。求 and actual case whether match; by is located land right nature; property status, whether has damage or quality problem; property using situation, rental or use; reference around similar property price, judge assessment value of rationality; whether exists property disputes, and seized, and freeze, and mortgage, and demolition, and transformation, limit situation. 2. to land right mortgage of, survey people should verified following information: land right card by contains Ming information (right people, and location, and nature, and term, and area,) and actual case whether match; land nature; land flat situation; ground buildings situation; reference around similar land price, judge assessment value of rationality; mortgage real whether has other mortgage right or notice registration established prior; whether exists property disputes, and seized, and freeze, and mortgage, limit situation. 3. other chattels, ownership, the value of the mortgage should be implemented, and whether factors such as easy handling. (C) pledge of collateral investigation procedures, investigators should enforce collateral value, convenience custody and disposition, pledge rights effective identification, registration, etc. (D) guarantee investigation to ensure that the procedures, the investigation shall, in accordance with the borrowers standards to investigate the guarantor evaluation assurance. 15th information audit survey people deal with borrowers and qualification provided by the guarantor, financial status, proof of identity, the authenticity of the data carefully reviewed, verifi