• 2022-06-19
    设函数[tex=17.429x2.786]tXWE0F6j++n50kWnSBRlwMZxvcRdzNMw2zMM8bdM1Kf8qoQVlcNHVAfMUYpcXg1j6e+QbQNd5U+OT9E2z+l3R91rHaf85KLUWlkQCmfZ2H0=[/tex][tex=1.286x1.357]VAHhaW1te0xvoqDVN54/dg==[/tex] 求偏导数 [tex=3.143x1.429]49UFtdxdDKQlKWZMhTPj6rPxiqh+tgJH/AQPOzyRggo=[/tex]和 [tex=3.429x1.571]35NvkV3X2zf5DVZgRc62o4pn1ewKbqvvgB8r0L4LscA=[/tex][tex=1.286x1.357]BEB68bP4vOVk/XYYizw11w==[/tex] 证明函数 [tex=0.5x1.214]gNOHIx2AGu3qP//Yn7oxrg==[/tex]在点[tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex]石微分;[tex=1.286x1.357]H6tHfFjOZ3ZWdB4qPQ9Ocg==[/tex] 说明偏导数[tex=3.143x1.429]49UFtdxdDKQlKWZMhTPj6rPxiqh+tgJH/AQPOzyRggo=[/tex]和[tex=3.143x1.571]35NvkV3X2zf5DVZgRc62o7adDA5nuJyCfNAVqkh6yg8=[/tex]在原点 [tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex]不连续.[ 此例说明定理 [tex=2.286x1.143]eDVSNWgs6+39HdRFlWu+jA==[/tex] 的条件(偏导数连续)不是函数可微分的必要条 件]
  • 解[tex=1.286x1.357]VAHhaW1te0xvoqDVN54/dg==[/tex] 当 [tex=4.5x1.429]jUTtlqzeBKWOBEjVaau28DK43LcSEV8tRedq4MKRF8s=[/tex] 时,按照初等函数求偏导数,即[tex=29.286x6.071]ifE9NWj3X6IpRVSt3T5ITiWEg71UF/QFvTJVtsYjAD4bkZkQOAC0/st6+YPTZL045XO4Au+gjJ+auw0pb+Tc2UApIOSGJxzK/vDXG0ff3xBnmr0YCT3oJSr6ztdxn4FJzm9uZW16I0bJUxecLkdAm6EOCEnbavGrFA+24Udkf4upvkBLnaYBOPb47SY4JWzKm1psslVDL8kFyWmLWwvDMoXBmcbrTcoZb8WKfnSjrYCODBEGDwprOtkSDwQSI7A4wL350lZcki2Adu9ivE5S56ic3GZDSz9G9EJj2XERwWw82sH87GbC4UX26zJcicJm5/ws0OUki8GSWuT3fc+nQPXTJvKiNiSfFK5bfRzacMGPD5ljk+tU4FtiTcBlB1KggcSTEiea5963ZI3C81vpSZDZDNdLu9nlw9+E6r12hpc=[/tex][tex=18.071x2.786]6Kyz8u2EAi1XLpIzn3Fu8fdXKjj12CABzguQH/EUZKgicbAxCTHGTrohLqbhvPtMsn8hZewM1pX5jDEOAJSDMSBVgCsKTbzhcPYjr+mnESgCfNiTsHkif9QJXnYXDuS3ua7ySqKrYrjbOEGwvsqy2g==[/tex][tex=21.5x2.786]35NvkV3X2zf5DVZgRc62o3aLli6nGq5BaJdrt8mqwhEsw2XRuXWDRG+Ve8hdJ+V2Fi3h6oa+6LzzqqmIb4BGWYHoGEdY27FidKCwUODwzpaDgrmvuObsMnE92DMZYlCRHlSxBKlulDENfmwOdNC1rdA7TzN08TWMAFk7TOHKe2Y=[/tex] 根据对称性 ] 而在原点 [tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 处, [tex=13.857x2.5]49UFtdxdDKQlKWZMhTPj6mZNF1ADi0D0Kz+gkTdKNzuDbpD+stn5YUNOsypfxFVoPAssnKK0p4xYdMAqlv+JjMxhFV2UjaVG5O9FrMrTWzA=[/tex]同理, [tex=4.643x1.571]35NvkV3X2zf5DVZgRc62oz6ElJZNynASZPsjB6Yny1M=[/tex][tex=1.286x1.357]BEB68bP4vOVk/XYYizw11w==[/tex]因为[tex=26.0x3.357]tlFxsIf78aAT6CS7PnNwkkDXZ3Uhq7etRBjSshMo2a3ggFPmo3hfeCuo9FzqTRlOALOShZ3U1uAHQqZ+CNSyZX03yY3PE4x3zJ3b02puDFyVfQlNPcSNwgZ1Exml/HGHV7lJecW2F21DIvn3pUgQt3+ruSnVBOk9RWwIBArbvM4DG2nDXIeGghpxxiLD0NFDKp99miCPwaKq37MaEdXqU2t3YGdSXuWW08U3gnz5z0TEcJK7zIlViA82RqdS6EJCQ+qdP/HmlYPhJJpbD5N8Ep6kZqgtvopF9e1cTzasbuWBlnwkmrBnEti+X66ETYokL2pJVIkHshEHqWy0nvESJQ==[/tex]所以[tex=9.571x2.214]11yPWWlYeqHyfvvm+OFL4oK8tycModIdySsuqQvYNX6YyiAvPJI3t1CNvvHI/+ax[/tex]因此,有 [tex=2.071x1.214]2UVXKNd1NTqhh+9YC1Iw1g==[/tex]和 [tex=2.071x1.214]/xCdtgpSjwti3+D2GvDusg==[/tex], 使[tex=22.0x2.214]dqdbduNXZkSIDRneer+0qbU1g823IYeMiTVpXtnRQ/sgS13WJbR0NgXzgKn+7jYzY6cx9xtuZyzqVPY3nHtWv2RQuiS7vQziaM6/xkQYBLvrsqacD93JG1iyFxXP7O3e[/tex]根据可微分的定义,函数[tex=2.786x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex] 在点[tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 可穀分.[tex=1.286x1.357]H6tHfFjOZ3ZWdB4qPQ9Ocg==[/tex]偏导数[tex=3.143x1.429]49UFtdxdDKQlKWZMhTPj6rPxiqh+tgJH/AQPOzyRggo=[/tex] 和 [tex=3.143x1.571]35NvkV3X2zf5DVZgRc62o7adDA5nuJyCfNAVqkh6yg8=[/tex]在点[tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 不连续,是因为它们在 点 [tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 没有二重极限. 事实上,当点 [tex=2.286x1.357]Vc2pH4ypHndnllKqCpRn1g==[/tex]沿直线[tex=2.429x1.0]iCWMESxH27wos2YIzODARQ==[/tex]无限接近点 [tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 时,不存在极限[tex=26.214x3.429]OtiKHStSOCVCGCaWj7ZqtufIOhWcjHSf69H+vKAaXHSyn7OPCavM/D+xwLE2ynO0zu1tb96w0DXSMoR/VAQVe1sYjHuI6+7PVv6Fj6NBB1tlmPGmF4entDE7o/gJW3yafb7uUR/zuVtHYvzJGaZInsE1oYJ/o0gQWBeSXVN45j2MrNUQ5fwI7YIAIn/suJuLosyJEXPPzAzA9+Isjo5MLmG/AhbSMczlqvxEAikDA4WnpeFZXGoHQfev0+AuqiTwQ1bw6nJtAEiblXtnBmG0ng==[/tex][tex=17.429x2.857]MiKRkUc+RA7d/dPkcEDJUg/KoiW0uH4gYZa2JWuSOq+WXsmO+o18zme3sblAoZ6djJ8kt7/uNx+oWjnu8AsOZ1dIZ9lGQPOymwN7DsgtVzit2m8hjEm/aCCBJSxnaqQxWHRWXPj9+2DmVYqugl0p27SbnFVErChNV7N7xSgQMdY=[/tex]

    举一反三

    内容

    • 0

      求函数[tex=3.286x1.429]kdT+eIE7CHPynuN6CaN40g==[/tex](抛物线)隐函数的导数[tex=1.071x1.429]BUw1BPFU3fsJlAl/vt9M9w==[/tex]当x=2与y=4及当x=2与y=0时,[tex=0.786x1.357]Hq6bf3CacUy07X+VImUMaA==[/tex]等于什么?

    • 1

      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 。

    • 2

      求下列函数的导函数:(1) [tex=5.0x2.357]X/CieCDGJ7iPQ3YFWuscHxHrcIE/dPFa9tFyiJXze8A=[/tex](2)[tex=6.643x1.714]Oj74y/L+OxY81QME5JWMcl+7PZ2FGQswwvjgVhjq1Dmb6dBU0oAjZBW7eFBVjqo6[/tex]

    • 3

      对于以下两种情形:(1)x为自变量,(2)x为中间变量,求函数[tex=2.214x1.214]sy9gaFRMGlrH59gm9bWSDg==[/tex]的[tex=1.5x1.429]5W5tOYbJ+LlsRP2dMsi4byxwtjvvL/3u7NEzPV5PWp0=[/tex]

    • 4

      设h为X上函数,证明下列两个条件等价,(1)h为一单射(2)对任意X上的函数[tex=5.429x1.214]3BrfPgAFe5dbHQTMAYnbS+118W4YAj6CiW06EKMaxNI=[/tex]蕴涵[tex=1.786x1.214]pxzkG5OdsKT9CiCwC5OvPQ==[/tex]