函数f(x)由下列表格给出：[img=507x101]1790264db51c3de.png[/img]用辛普森法计算积分[tex=5.643x2.786]D4fJ7kgp/Pt7EgwBLk0AsDgagOGD8LqIozY8PGV5Hj0=[/tex]的近似值（精确到小数点后三位）
函数f(x)由下列表格给出：[img=507x101]1790264db51c3de.png[/img]用辛普森法计算积分[tex=5.643x2.786]D4fJ7kgp/Pt7EgwBLk0AsDgagOGD8LqIozY8PGV5Hj0=[/tex]的近似值（精确到小数点后三位）
[tex=2.929x1.286]p3y2AkBvj4VeXD0t3hDKhg==[/tex][tex=5.643x2.786]fnpmC2J6JmQBLyo5NmGAz59F3pyik8ld9oy48ECqU/bYeGOB5vE6MZIj8IpVJfYK4NqwaJ4hKFkLNruPIMSiEjUwIH7DqqcU5OU+XncOsrQ=[/tex][tex=8.571x1.286]7fy022pG1T/P4ds8fOkd9ciCLV1+94P9pTo4ODRWHN4pyy1C9bVnKthNTQFoozT6[/tex]
[tex=2.929x1.286]p3y2AkBvj4VeXD0t3hDKhg==[/tex][tex=5.643x2.786]fnpmC2J6JmQBLyo5NmGAz59F3pyik8ld9oy48ECqU/bYeGOB5vE6MZIj8IpVJfYK4NqwaJ4hKFkLNruPIMSiEjUwIH7DqqcU5OU+XncOsrQ=[/tex][tex=8.571x1.286]7fy022pG1T/P4ds8fOkd9ciCLV1+94P9pTo4ODRWHN4pyy1C9bVnKthNTQFoozT6[/tex]
计算积分[tex=5.643x2.786]3iz5F64DB14PhYI5E6lSqjmpZzN9ROkMVtT8kAT3qJ656PxVohOmPHakjxmooYg+urMJIwDL8UOZTGddVJCQ1w==[/tex]，其中[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]为整数。
计算积分[tex=5.643x2.786]3iz5F64DB14PhYI5E6lSqjmpZzN9ROkMVtT8kAT3qJ656PxVohOmPHakjxmooYg+urMJIwDL8UOZTGddVJCQ1w==[/tex]，其中[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]为整数。
判别[tex=5.643x2.786]D+OdHpWjBNPXoMUoCawgfhnpy1BSg9AGq3/Nj6HlJel2VUyIWutszdFdX7xgtX62[/tex]的敛散性，如果收敛，计算反常积分的值
判别[tex=5.643x2.786]D+OdHpWjBNPXoMUoCawgfhnpy1BSg9AGq3/Nj6HlJel2VUyIWutszdFdX7xgtX62[/tex]的敛散性，如果收敛，计算反常积分的值
假设以下供给和需求方程描述了一个市场:[tex=5.643x2.786]oGAW4m++pPFV3ksPwn8f2P8hAAIkHoxcT5j6/0NYG3NjCOy1UE66T1JGob7X7A5qsLhfz9rvbETvbloBwGnWpXV+UUJ7aqVigRrbBrtbnbqE0vMccybRFzVcQ7dxXVcR[/tex]求解均衡价格和均衔数量。
假设以下供给和需求方程描述了一个市场:[tex=5.643x2.786]oGAW4m++pPFV3ksPwn8f2P8hAAIkHoxcT5j6/0NYG3NjCOy1UE66T1JGob7X7A5qsLhfz9rvbETvbloBwGnWpXV+UUJ7aqVigRrbBrtbnbqE0vMccybRFzVcQ7dxXVcR[/tex]求解均衡价格和均衔数量。
试说明下列各量的物理意义 (n 为分子数密度, N为系统总分子数).[tex=5.643x2.786]eBsHs8yOhiL8vy7olawOHspQJQTWWMdSYbqSd5kRTbfmP3UyYk/5OJKVephjpJ6y[/tex].[br][/br]
试说明下列各量的物理意义 (n 为分子数密度, N为系统总分子数).[tex=5.643x2.786]eBsHs8yOhiL8vy7olawOHspQJQTWWMdSYbqSd5kRTbfmP3UyYk/5OJKVephjpJ6y[/tex].[br][/br]
将下列函数在指定点展开为 Taylor 级数，并给出其收敛半径:[tex=5.643x2.786]8Xpgx5GZy6PrbxRVDDeTKkwPPssal8AIY5s0G5xIyFX4GmFAHZbzIrn8kPX3GG5S[/tex]，在[tex=1.786x1.0]iYbK/m2HPL4SyxgIH2UTBA==[/tex]展开( 可只求前四项) .
将下列函数在指定点展开为 Taylor 级数，并给出其收敛半径:[tex=5.643x2.786]8Xpgx5GZy6PrbxRVDDeTKkwPPssal8AIY5s0G5xIyFX4GmFAHZbzIrn8kPX3GG5S[/tex]，在[tex=1.786x1.0]iYbK/m2HPL4SyxgIH2UTBA==[/tex]展开( 可只求前四项) .
代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：在[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]中解下面方程组[tex=5.643x2.786]7EJHVCtO2IWq3KpdB+jQshTaqXo3Uympm4jwsW/qmipi9+bSbIt86pEFPvVXo19v/FDiPp/oc1SCkyteavXREtOye/NmkBTluPV1MJf26H0=[/tex]
代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：在[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]中解下面方程组[tex=5.643x2.786]7EJHVCtO2IWq3KpdB+jQshTaqXo3Uympm4jwsW/qmipi9+bSbIt86pEFPvVXo19v/FDiPp/oc1SCkyteavXREtOye/NmkBTluPV1MJf26H0=[/tex]
代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：在[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]中解下面方程组[tex=5.643x2.786]7EJHVCtO2IWq3KpdB+jQshTaqXo3Uympm4jwsW/qmipi9+bSbIt86pEFPvVXo19v/FDiPp/oc1SCkyteavXREtOye/NmkBTluPV1MJf26H0=[/tex]
代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：在[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]中解下面方程组[tex=5.643x2.786]7EJHVCtO2IWq3KpdB+jQshTaqXo3Uympm4jwsW/qmipi9+bSbIt86pEFPvVXo19v/FDiPp/oc1SCkyteavXREtOye/NmkBTluPV1MJf26H0=[/tex]
代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：在[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]中解下面方程组[tex=5.643x2.786]7EJHVCtO2IWq3KpdB+jQshTaqXo3Uympm4jwsW/qmipi9+bSbIt86pEFPvVXo19v/FDiPp/oc1SCkyteavXREtOye/NmkBTluPV1MJf26H0=[/tex]
代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：在[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]中解下面方程组[tex=5.643x2.786]7EJHVCtO2IWq3KpdB+jQshTaqXo3Uympm4jwsW/qmipi9+bSbIt86pEFPvVXo19v/FDiPp/oc1SCkyteavXREtOye/NmkBTluPV1MJf26H0=[/tex]