?2?y??y?2xsin2xx1P?x???,Q?x??2xsinxx 11???dx??dx??lnx?lnxy?ex??2xsin2xexdx?c0??e2xsin2xedx?c0???1???x??2xsin2xdx?c0??x?sin2xd2x?c0?x??cos2x?c?x??????3.求解下列微分方程的初值问题：
?1?y??e2x?y,y?0??0dye2xy1?y,edy?e2xdx,?eydy??e2xdx,ey?e2x?c dxe21111Qy?0??0,?1??c,c?,即ey?e2x?2222?2?xy??y?ex?0,y?1??0yex1exy???,P?x??,Q?x??xxxx11xx??dx?edx????lnx?elnxxxy?eedx?c?eedx?c??????x?x? ??x?11xlnx?1?ex?exdx?c?edx?c?e?c??????x?x?x??Qy?1??0,?e?c?0,c??e即y?1xe?e??x4.求解下列线性方程组的一般解：
?x1?1????x1?2x?1?2x3?x2?x2?3x3?5x3?x4?2x4?3x4?0?0?0?102?10??102?10???①+②????01?110??A???11?320????①?2+③?0?19?50??2?15?30??????10?②+③??01????00???1?③??-2?+①??0????③+②???0??2x1?2???x1?x?1?x2?2x2?7x2???102?10?2?10?1??③?8???01?110??110??????18?40??0??001??2???0000??x1?0??11?0???x2??x4?x4是自由未知量?10??22??11 0??x3?x401?2??2?x3?x3?4x3?x4?4x4?11x4?1?2?5?2?1111??0?53?7?3???②??-2?+①??A??12?142??????12?142②??-1?+③???17?4115??05?373??????12?142??12?142??1???②????373??①+③?5???????0?53?7?3???????01?①,②?555??00000??00000?????164??10?1555?????x1??4?x3?6x4?373??5②???2??①??????01?,??x3,x4是自由未知量??1555????x2??3?3x3?7x4??000005????? ???x2?5x3?4x4?2?x1?2x?x?1?x4?3x3?12有解，并求一般解5.当?为何值时,线性方程组?3?x3?x2?x2?x3432?1??7x1?5x2?9x3?10x4??2??1?1?54?1?1?542???①??-2?+②??3?9?131011?31?2③+-3?①??????????A??①??-7?+④?0113?9?3?2?233??3? ?????7?5?910???0224?18??14??108?5?1??108?5?1?②+①?????②??-1?+③0113?9?3??0113?9?3?②??-2?+④???????③,④???00000??0000??0000??7?????7??00000??当??7时有解,为??x1??1?8x3?5x4?x?x3,x42??3?13x3?9x是自由未知量?4?x?x2?x3?16.a,b为何值时,方程组?1?x1?x?2x?23?2有唯一解、无穷多解或无解?x1?3x2?ax3?b?A??1?1?11??11?22??1?1?11??1?1?1①??-1???????+②①??-1?+③??02?11?????②??-2?+③??02?1?13ab?????04a?1b?1??????00a?3当a??3时，有唯一解当a??3,b?3时，有无穷多解当a??3,b?3时，无解7.求解下列经济应用问题：
?1?设生产某种产品q个单位时的成本函数为：C?q??100?0.25q2?6q?万元?，求：①当q?10时的总成本、平均成本和边际成本；②当产量q为多少时，平均成本最小？①C?10??100?0.25?102?6?10?185?万元?C?q??C?q?q?100q?0.25q?6,C?10??10?2.5?6?18.5?万元?C??q??0.5q?6,C??10??11②C??q???100?q2?0.25,当C?q??0,即q?20单位时，平均成本最小1?1?b?3???
?2?某厂生产某种产品q件时的总成本函数为C?q??20?4q?0.01q2?元?，单位销售价格为p?14?0.01q?元/件?，问产量为多少时可使利润达到最大？最大利润是多少？R?q??pq??14?0.01q?q?14q?0.01q2L?q??R?q??C?q??14q?0.01q2??20?4q?0.01q2???0.02q2?10q?20L??q???0.04q?10,令L??q??0,q?250?件?L?250???0.02?2502?10?250?20?1230?元?
?3?投产某产品的固定成本为36?万元?，且边际成本为C??x??2x多少时，可使平均成本达到最低？?C??C??x?dx???2x?40?dx??x2?40x?446664?40?万元/百台?。试求产量由4百台增至6百台时总成本的增量，及产量为?100?万元?
C?x???C??x?dx?c0???2x?40?dx?36?x2?40x?36C?x??C?x?x?x?40?36?36,C?x??1?2,令C??x??0,x?6?百台?xx?4?已知某产品的边际成本C??q??2?元/件?，固定成本为0，边际收入R??q??12?0.02q， 求：①产量为多少时利润最大？在最大利润产量的基础上再生产50件，利润将会发生什么变化？①L??q??R??q??C??q??10?0.02q,令L??q??0,q?500?件?②?L??
550500
L??q?dq??10?0.02q?dq??10q?0.01q2?550?500??25?元?500550
电大数学形成性考核作业答案完整版准确版
