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27考研笔记——微分学最“抽象的题目”相关变化率

  • 2026-04-01 08:30:48
27考研笔记——微分学最“抽象的题目”相关变化率

27考研笔记——微分学最“抽象的题目”相关变化率

这个看似不难，实则很绕，没有正确思路很难得出正确的解，和积分学的物理应用一样，必须积累思路找到突破口
留下关注，我会在更新积分学笔记时展示积分学的物理应用#抽象题#抽象数学题解析 #27考研人###

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      1. CONNECT:[ UseTime:0.000565s ] mysql:host=127.0.0.1;port=3306;dbname=www_sjds;charset=utf8mb4
      2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000899s ]
      3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000299s ]
      4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000423s ]
      5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000458s ]
      6. SELECT * FROM `set` [ RunTime:0.000218s ]
      7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000601s ]
      8. SELECT * FROM `article` WHERE `id` = 469113 LIMIT 1 [ RunTime:0.005960s ]
      9. UPDATE `article` SET `lasttime` = 1775078319 WHERE `id` = 469113 [ RunTime:0.016592s ]
      10. SELECT * FROM `fenlei` WHERE `id` = 64 LIMIT 1 [ RunTime:0.001705s ]
      11. SELECT * FROM `article` WHERE `id` < 469113 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000468s ]
      12. SELECT * FROM `article` WHERE `id` > 469113 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.001005s ]
      13. SELECT * FROM `article` WHERE `id` < 469113 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.002044s ]
      14. SELECT * FROM `article` WHERE `id` < 469113 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000721s ]
      15. SELECT * FROM `article` WHERE `id` < 469113 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000776s ]
      0.111152s