设曲面 [tex=0.643x1.0]jLbabU9pW65GUKemsNBJWw==[/tex]在一点的两两夹角为[tex=1.357x2.357]pEZoD8oN+U8NaaGKSpBaGwiJp3ocz6HgaagdSyBZmEM=[/tex]的[tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex]个切向量所对应的法曲率为 [tex=5.714x1.571]VxtZSlWBZgV1WZxmvQ8tQNHsO+xmZ/IfAiDCMgGDFMfN2Ge3iGe4CVCXx8s4NPcU[/tex].证明: 当 [tex=2.714x1.071]v3C7CemUdmHynh0e75zv8Q==[/tex]时有[tex=10.714x2.357]oE+8fjh23GvpQ9XbKbwpVifkvPAzPVCrGpKfwqoSpOtJO/0ak7Ze7qEb2QuCxSpMrntePIxiaSMYo7zt/XMS3w==[/tex].

2022-07-23

设曲面 [tex=0.643x1.0]jLbabU9pW65GUKemsNBJWw==[/tex]在一点的两两夹角为[tex=1.357x2.357]pEZoD8oN+U8NaaGKSpBaGwiJp3ocz6HgaagdSyBZmEM=[/tex]的[tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex]个切向量所对应的法曲率为 [tex=5.714x1.571]VxtZSlWBZgV1WZxmvQ8tQNHsO+xmZ/IfAiDCMgGDFMfN2Ge3iGe4CVCXx8s4NPcU[/tex].证明: 当 [tex=2.714x1.071]v3C7CemUdmHynh0e75zv8Q==[/tex]时有[tex=10.714x2.357]oE+8fjh23GvpQ9XbKbwpVifkvPAzPVCrGpKfwqoSpOtJO/0ak7Ze7qEb2QuCxSpMrntePIxiaSMYo7zt/XMS3w==[/tex].

答案：

设 [tex=3.143x1.357]HKxOQjrLFlyPuOzE9lKKS8scaBm1Vl/4cpU7xBqYdPmW+tEWwdvAMrOGmvWoTHja[/tex]是在一点[tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex]的两个彼此正交的主方向单位向量，对应的主曲率为[tex=2.214x1.214]MExkfQnfhNUqjVMjT4IYtg==[/tex],.[tex=0.929x0.786]o6X45tpG/qifjWfiPhyOpQ==[/tex]个切向量为 [tex=4.714x1.5]u3Nwbv8J5CLiCRqf9yxPXnlVPY8a1M3q1EeQrodFB7rkq6Rx9Z7gdKzg9rMTJhTw[/tex], 其中[tex=1.0x1.5]boIX8AAX2XsJHWHG2XY0Ug==[/tex] 与[tex=0.857x1.214]m5prVqiOIF/fkw29IVTpjQ==[/tex]的夹角为[tex=0.5x1.0]qm+hGi0qngLh1B7HsENMPg==[/tex], 则[tex=9.786x1.571]8Zertxn1NIRMdqBO/ET6NxuL9tdFvUEH+PP2En8wFRv+gqCIE8+v4mHs52qTdvfjmTEPfJP6DNzy4cF6iafFhA==[/tex] [tex=27.643x2.786]MlI5KHjinuMHO/y7MrLceS6gY9BBl4bwFrPBoemOs58bDrT8Fh2OuUv6VHZZo1E2ZHdMoifh9eCQXMB0xCuqrjVtajBdIQ4ZdisS1L4b0p5t9Q+F8grRxQvithALrjhfy4L4ucgSdo5tuO5iNEgE65kzgFToDq4CRfvlL3yTCxuB3xaqPVaexhlsc+gWhyClSbLnjb8q+6b7ECAMTxr9bQ==[/tex][tex=33.571x10.0]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[/tex]又[tex=28.714x11.214]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[/tex][tex=21.286x2.714]ufGyx9MKAb9zxnOd2ZxvRUcTHustDi1rUdjEn/vWMJLqFVV0Lp195b2oVrqo+3o0nE+X+Jma82Luy41YClw4ZUmT9oGdqLN09rQ5tXhNpMTfsnefHXiCjjxEG2WGqum6Wttv/OOggtNV8hMlIwVees/aeVK8GRsUZHy+TJ/YpNJ0SGOxZQn2k9bnm4mD7tom[/tex].

举一反三

内容

0
对 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]的不同值，分别求出循环群[tex=1.143x1.214]StMMJ6qThnpokZJIPGrdFyP3vrLnUdltYxmLxjw8za8=[/tex]的所有生成元和所有子群。(1) 7; (2) 8; (3)10 ;(4) 14 ; (5) 15 (6) 18 。
1
假设“☆”是一种新的运算，若3☆2=3×4，6☆3=6×7×8，x☆4=840(x＞0)，那么x等于： A: 2 B: 3 C: 4 D: 5 E: 6 F: 7 G: 8 H: 9
2
设[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]是 3 阶矩阵，且[tex=2.643x1.357]h0pLE8vvleI3SS/lZLfCsw==[/tex]，则[tex=4.143x1.357]TzVoItsLVWI00YVI4rvLQQ==[/tex]( ). 未知类型：{'options': ['2', '-2', '8', '-8'], 'type': 102}
3
判断半径大小并说明原因:(1)[tex=1.071x1.0]ZIxpATrL2EWTpYe3CKPlpg==[/tex]与 [tex=1.357x1.0]LO7mudz7++HOXb8YDQ1UtQ==[/tex](2) [tex=1.286x1.0]nOvFdt4hpTubfX23eRvSvg==[/tex]与[tex=1.071x1.0]Kr2c9X1cZ4El5JSNMoM0/w==[/tex](3) [tex=1.214x1.0]Q1mlMfKWwfAuQJLgzt2cVQ==[/tex]与[tex=1.357x1.0]ovKrdUm5wnQSTfl9He3wzA==[/tex](4)[tex=1.143x1.0]8nY7k4VEnlDIEx7o05iMhQ==[/tex]与[tex=1.357x1.214]in11+JirBe0MeyXDnVwAww==[/tex](5)[tex=1.643x1.214]cIgqspnlK9Ra13rNdyZhHQ==[/tex]与[tex=0.643x1.0]jLbabU9pW65GUKemsNBJWw==[/tex](6)[tex=1.929x1.143]CtrLAecFBVyCnMYbqB02Ag==[/tex]与[tex=2.0x1.214]2cEIifUWf5oYRzhjCpTV6A==[/tex](7)[tex=2.214x1.214]OdTls2gllRl/Z1zy0+35/g==[/tex]与[tex=2.071x1.214]YDXlUgl4Yvd6QFjcd0Ns2Q==[/tex](8)[tex=2.071x1.214]QvCjZKA7OQkNYccCl0MVgQ==[/tex]与[tex=1.929x1.214]GDfkuEdqfBLP2oRgr+Wojw==[/tex]
4
求下列函数的单调区间、凹凸区间、极值点、拐点和渐近线,并绘图(图略).(1) [tex=6.643x1.5]bfylM61K4fB2dxr0OSsfGnNoGCHA31PVTv+V6O1K8rw=[/tex](2)[tex=7.643x1.571]v8BogKFXW30N+HMJ7QR6DhxEDs5D0riUpoj095rhlGc=[/tex](3) [tex=3.714x2.143]X1YpNX45Pb+t3RD9Lv2Xa/npVx6iPUE04M2Y4K2k/cw=[/tex](4) [tex=5.071x3.0]4TWEbfJ+QFPbBo6PXWTsCrjc66tVrHBOTlDUBxhSpARz8/MfCO/nUo/gE3SyIffw[/tex](5)[tex=6.571x2.429]gt+k1kCw/+VFBVaKddmG6PvDvxiTdyZFXDwIPBeuGlw=[/tex](6)[tex=5.643x1.429]Hzyd6Qvm69qjRqgBIuKTx/cTmFyy56Dt2K/GC7NoCdc=[/tex](7) [tex=7.143x1.214]CwtdUElTamN1NqF0aKHeWGdaXEazoOnz3w3c67izzuE=[/tex](8)[tex=4.714x2.786]cxjZEag+Wbr67lAUIC3Slk2OV17yHgezOhFRferr5F0=[/tex].