证明: 在点[tex=5.571x1.357]5Mv5IhIrcJ0jOelk3DLzinCcGeiQtnSTWnWEClUYx3wrZmO9qiXYsIPL/ySUCbeS[/tex]处,函数 [tex=7.071x1.429]KpCP3f0yVC1ooWVQ1GpC5AgDfjLhpIzDvQfU0AtIPx4=[/tex] 及 [tex=14.357x1.429]5ChPGZLNHqZ2PJedvGqfxAxoJejfwmj8UEo91VMICziSY7n9DkUrSmXOJv/y10oW[/tex]([tex=5.643x1.214]f5gS3rEdYpfc+EroQpRocfRUIBa1BitrODaSh0qwmps=[/tex] 为常数且 [tex=6.0x1.429]2sjA3UQL9lu84Vtwa9TxanERn8skFytJiwaw6DZmmM8=[/tex] )二者的梯度之间的角度当点 [tex=1.357x1.214]nVlWDiaq/AF5IB+/Nxj18A==[/tex] 无限远移时趋于零.
证 本题的题设条件“点[tex=5.786x1.357]GIZCj4CU+8jNGJF/dolyu6McuAqmKnU7qz7gQPH/e7RnY4gEscsuaWoziLuBWMFK[/tex] 无限远移"应该理解为 " [tex=9.5x1.0]q0IuwAtP0HWZOR6ffQwHiwg87zJZr/B8x65xNdbWoAUB1WUdUHCJE3JhHYULIx2bi9UmLkWpLnxcmqS6HhSwhhSYVv1nxEjzVThgyJ30hGI=[/tex]同时成立"(此时[tex=13.429x2.214]wceT8erhp8GRvtj5GFPsbRb0kAP4ZTEBs5ex+Uo4C1QGSFDknNX2icsFXxgJj/iBV7eee3w4S+kIdmfqrIE4dHcbEkggX2V2Jcouk/f6Of4+x3W6YKiFiSW9KXmM84dE4J7S5667ju75N2r0c6gwlw==[/tex]). 否则, 本题的结论不成立.显见有[tex=29.429x1.357]79Wd/JsaQKi3RBB3vwr83yUNUh/dlJkn9kb66Vshlxg3uyvn7gfk/Y3guWFmdDocL3LSrH9wi3T0LeqWtJAkRQdDD0sKulh7TxCjMngfX1Tt/auxfwvJWV6rNDV4QGCV/jZBqKMBTDvRDdWkGHGTzE5sSUYK4dAmB8Phxz7T+VAIF3Ce0+gTHIJeCmGm+dcUPsH8cCQbA5DibpyC6Z+tv/tnnGgaJkPqOy/UIOMJY2Y=[/tex]令[tex=22.714x2.571]wFR9a4OKBwGrU9swjM3YKW9ZQ1VwBBUuPytiw2pBS2oe47g/MHs/UgJFV1nJABWno4M5FnwMSZdy+v+1XFPICGfF2/IVKAkpgrVEi0d/URIIqA6ZGGDQ31QqPVMIJ8DAsIRp0thKPfDB8xOErM67SAVlLzFoeQnStbaeuY9D9hLEaXOiDkexhSHWfp/rcGzpsgtODpJjpK1XqK4KRir8Iw==[/tex]于是, [tex=2.714x1.214]5YOe7r6oTucK/XddOhmUaBp8BS5PdlAQcHAkjd84du4=[/tex] 与[tex=2.5x1.214]ADunzeE2TBtwuRfQOtgYCQ==[/tex]的大角 [tex=0.5x1.0]qm+hGi0qngLh1B7HsENMPg==[/tex]满足[tex=15.214x2.857]lqcL2KO1O6LsIXhyfN+Kv/EZbrrWXizuT/RI9pIgNrhtjZ7Ln27zbfxBvD+Ah5cnEGrrSz3s/ai4r3Vfd+7o6cSUGPiiLcrPxc3h4EEj2a+fXwINGOm8VL86LLyTCWUlbwulOOIjO84TxgZsdfQ680nrB6u4cXdafFvmbsSVApAoo0RgK6O3ZOOx0FDNd9f88evXMXpSVQv042VYfCH/c35ZE4KksJLyx3Ox1WHgNYI=[/tex]或[tex=34.429x6.286]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[/tex]令 [tex=19.357x1.357]hC585hKChVbycc8LeCFdB67kzMoTEStAsPJJhoyvI7KrzbOJcMf+V6jkrZ/pRMt4wOTOIHn/WF3V8NtGYnXVQBApuQLSILHqVmElnU1hz+BXTyqNvg7cDGfv4dEf9xWlYOs/jD/j1waNedjJ6N8R8UGnLMnup4APoFnmK0wPb6o=[/tex], 则[tex=10.571x1.643]3QCXKv32G+RxjlkwK9QRyjuHz0gms0X0HZbp1/kpghVZG2iKfPO+fC3M2PxQqA6GMK9EtDj9Jha6K73cO0ElIOCG3oNFA3gaFUKqXgPiI3ej0k0foPE1uxLIc9CItmDO[/tex]于是, 当 [tex=8.429x1.643]hqMBEP95Ryq9piZ9/5t1N8fYJuvUWy94tQqYMGlae+BPKOa41T/9BtHACC2GfRSVlo6yUD6OJOd5nBWHcYdCYg==[/tex] 时,[tex=3.286x1.143]95HKWxSUubIry3sXWGBOpZnxs5AhK/9jhZskGTWk508=[/tex].再令 [tex=8.786x1.357]gARTuYfTsLW18bQj27O6Eg63Gs+s4t1piKOaE7GQ1Qw=[/tex], 则下述不等式显然成立[tex=20.071x5.857]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[/tex](当 [tex=3.286x1.143]95HKWxSUubIry3sXWGBOpZnxs5AhK/9jhZskGTWk508=[/tex]时 )[br][/br]于是,当[tex=8.429x1.643]hqMBEP95Ryq9piZ9/5t1N8fYJuvUWy94tQqYMGlae+BPKOa41T/9BtHACC2GfRSVlo6yUD6OJOd5nBWHcYdCYg==[/tex]时, [tex=3.786x1.214]kBtmwzpYJS6X4ihguleuJEFEiel4LzNLmDA6I7nzFRNjZdlobvezYWBFnvVIu/5X[/tex], 即当 [tex=10.857x1.643]hqMBEP95Ryq9piZ9/5t1N8fYJuvUWy94tQqYMGlae+BPKOa41T/9BtHACC2GfRSVl7o87ah0RkWBWL0UdV5sNRo2M/6+wZ04/K391dk6SF9eg7bkc/ZB/n0HK9uCsw5d[/tex] .证毕.
举一反三
- >>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']
- set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为？ A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
- 若:(1)函数 f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数;(2)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]有导数;(3)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数及函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数,则函数[tex=5.643x1.357]GmtX7Vop79exGU/rpqXUYw==[/tex]在已知点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]的可微性怎样?
- 6个顶点11条边的所有非同构的连通的简单非平面图有[tex=2.143x2.429]iP+B62/T05A6ZTM0eeaWiQ==[/tex]个，其中有[tex=2.143x2.429]ndZSw3zT0QTOVLVdoUto1Q==[/tex]个含子图[tex=1.786x1.286]J+vVZa2YaMpc6mJBbqVvWw==[/tex]，有[tex=2.143x2.429]lmhx48evnQMhi03NovPXig==[/tex]个含与[tex=1.214x1.214]kFXZ1uR8GjycbJx+Ts2kyQ==[/tex]同胚的子图。供选择的答案[tex=3.071x1.214]3KinXFh3SXhZ7nIe1y9KEV6aadxhhJWeEy6Dij1iObdMUZkY6ZA5J2dVVjPSuhEf[/tex]：(1) 1 ;(2) 2 ;(3) 3 ; (4) 4 ;(5) 5 ;(6) 6 ; (7) 7 ; (8) 8 。
- 【单选题】请用地点定桩法在4分钟内记忆数字。 4 0 1 3 6 3 5 1 9 8 8 9 7 2 9 3 0 9 5 3 1 7 7 5 2 3 3 0 5 0 1 4 1 3 8 3 5 7 9 7 (5.0分) A. 已背 B. 未背
内容
- 0
【计算题】5 ×8= 6×4= 7×7= 9×5= 2×3= 9 ×2= 8×9= 7×8= 5×5= 4×3= 5+8= 6 ×6= 3×7= 4×8= 9×3= 1 ×2= 9×9= 6×8= 8×0= 4×7=
- 1
set1 = {x for x in range(10) if x%2!=0} print(set1) 以上代码的运行结果为？ A: {1, 3, 5, 7, 9} B: {1, 3, 5, 7} C: {3, 5, 7, 9} D: {3, 5, 7}
- 2
某人对商品x的需求函数是[tex=5.214x1.214]0m6eBd5eyK0NjuxeKfwtIw==[/tex]，[tex=4.214x1.214]I717YsPbj8Rnym1v2XQ+sFNkUl7mqUsGwbjwjXmy2xc=[/tex]，这里[tex=0.571x1.0]Za328cIB4SeR7rrzY+MM5Q==[/tex]是[tex=0.571x0.786]ZSLOI4fiO1oAbVC5M8IVkA==[/tex]的价格。如果商品x 的价格是0.5元，那么他对商品x的需求价格弹性是 未知类型：{'options': ['-10', '- 1/5', '-1/10', '\xa0- 1/3'], 'type': 102}
- 3
set1 = {x for x in range(10) if x%2!=0} set1.remove(1) print(set1) 以上代码的运行结果为？ A: {1, 3, 5, 7, 9} B: {1, 3, 5, 7} C: {3, 5, 7, 9} D: {3, 5, 7}
- 4
[tex=22.0x1.357]LHJ+y85YXU3v8GHWdrdQw3Wkm42jO1uuQ9ReIJQjcZKuQS9dt8xQcTgSBjKkS3fb[/tex][color=#000000][b],[/b][/color][color=#000000][b]求 [/b][tex=3.143x1.214]oFObQtwM9vyjjWL7fjyhww==[/tex][/color][color=#000000][b]全不发生的概率.[/b][/color] A: 3/8 B: 7/9 C: 5/9 D: 5/8