设（1）函数[tex=2.857x1.286]tj1rvgP4AHIdbrLux0kAEQ==[/tex]于[tex=6.0x1.286]fjJAzWZtJs19NgfzEJQ8oL4NXi+f4XlFwMPX3bGqJus=[/tex]内是连续的；（2）函数[tex=2.071x1.357]eAvaTAXWWX5VwHAZCgurVQ==[/tex]于区间[tex=2.571x1.357]sjdPs/hhXAmvACj9h5RVRw==[/tex]内连续且[tex=5.786x1.286]ZtVoL2TPCOybj66A3npvNbhJeYGp4hNc/LvOUnJk++o=[/tex]，证明：函数[tex=7.071x1.357]/w6TAplo7xn6TT9r64StC51ve9r5I6ONL24sJHt6ps8=[/tex]在区间[tex=2.571x1.357]sjdPs/hhXAmvACj9h5RVRw==[/tex]内是连续的。

2022-06-30

设（1）函数[tex=2.857x1.286]tj1rvgP4AHIdbrLux0kAEQ==[/tex]于[tex=6.0x1.286]fjJAzWZtJs19NgfzEJQ8oL4NXi+f4XlFwMPX3bGqJus=[/tex]内是连续的；（2）函数[tex=2.071x1.357]eAvaTAXWWX5VwHAZCgurVQ==[/tex]于区间[tex=2.571x1.357]sjdPs/hhXAmvACj9h5RVRw==[/tex]内连续且[tex=5.786x1.286]ZtVoL2TPCOybj66A3npvNbhJeYGp4hNc/LvOUnJk++o=[/tex]，证明：函数[tex=7.071x1.357]/w6TAplo7xn6TT9r64StC51ve9r5I6ONL24sJHt6ps8=[/tex]在区间[tex=2.571x1.357]sjdPs/hhXAmvACj9h5RVRw==[/tex]内是连续的。

答案：

证明  任取[tex=4.571x1.286]MMoXKf1LP2CDCvjZE5zoj0qMDMXpNxSr5nwZEBSnQOs=[/tex] [tex=8.286x1.286]1nvOIbVqymJoN7okmiiJRF2r3nuLcPMV69jLlid454G14ouO9exeIC82rLVdlg+d[/tex]，对[tex=2.786x1.286]joguGSInidzw2xc+WzmvAZad/jjxgQdNyh+mayOOv3Y=[/tex]，由于[tex=2.643x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex]在[tex=2.857x1.357]EZ1YLh+FMEcQAjNnWDBjTOIsNztTlNE8eiBgVShrvuw=[/tex]处连续，故[tex=2.857x1.286]6XWrGbUTgRaSPR9Pp+OJON+BrWCKWy3SgVd6SZygpgE=[/tex]，当[tex=9.429x1.286]u2i4zTueOksKj9UefMjY22Y40/5mBcL1gpkF3ZzQYquH8XOnW+G6TBVWa7rGjz4k[/tex]，[tex=9.0x1.286]+yORN7+bWIXMRpw/aFQf0JX3lE4+FNgfHbznmsgxp/l8K+9R/puGmrES0E1CscSW0uUnoHrhvGnqQ3Sb0hD5lg==[/tex]时，有[tex=9.857x2.143]++efK6GtIxbdXGxxw4AO3MGRXfqEdUamrUrm8gh+0uMO0i5hFY39Z7lR3jfqwC4eHHAZXY+pOe8xiekqyUgrWCOAt9EWwEdY6DMYV7DJlc0=[/tex]，对上述[tex=2.357x1.286]mlhEedFsgh4h9ok3HK/njQ==[/tex]，由[tex=2.071x1.357]eAvaTAXWWX5VwHAZCgurVQ==[/tex]在[tex=0.929x1.0]mQGdf3XTfQx0Qped0rrM9g==[/tex]处连续，故[tex=2.643x1.214]zlKeabRmX2Dxj8dDdgdiwCjG1cQR47j4RLY2/pAX76I=[/tex]，当[tex=4.143x1.286]7P27ElF/XcaZ/oZAaKggwhbN8WpuqaadfdAEx6G/9Zk=[/tex]，[tex=5.429x1.286]+MU+B/CvRtOkgbyuBZk45NUZLYv/j/XNEl9VkLe4bPGHwVDFQzQSZzH8Ebqr0T5t[/tex]时，有[tex=7.714x1.357]R9Ju8zbv7uvlitdme3sMwOLazvRLNhReoq7ZTgDbYE9sSK0ogmoTliWuJUjdhYZg6ZjPwjwl2UjWyzYEtVvcMQ==[/tex]，取[tex=6.357x1.286]whc5y+bVb2gvP9xKLfmDAsn7yi6+JaBs4F8NkaGFxWI4n+easBUXj4F8FFJTzfzmDNwYfBqet0s2o6vjcD22oQ==[/tex]，当[tex=4.643x1.357]zj2GP2WPSjSnFOWO8DtwKVcg8eUqb7o6avI6BQJPplM=[/tex]时，有[tex=4.143x1.286]azkORRxJwPtgk32XhIHbN85rPw1wW/I1Is6oB1ZPf3s=[/tex]，[tex=13.643x1.286]HqleCHteVrwjwsU/jQHi20O4jD7byTUV6Axho1Hp1Jj7kbXGN9KkDqZrxP7vFtWWvZ01PIhtAAA1CfBrCiJXVIQY5HX5xuV8w5tl2eMWDpxTFafL27CZH6KRipk2gAHykAkeHXn/Sp5jMzOeBx/4mg==[/tex][tex=19.143x1.286]iiDVbl8FroeNSws8uPUu+L+sPlLCytve9y9kF0viYLYqcaxzR9UVvKr6LulWs3erumAA4QdqDmyaf57e+1ltEXZ4xV64jmFkU/39y0WRK1S4SUPBnxt56YZLkMNpikFnyqYq8GglSNPPLtGJiX20ezSwdYC6vpSK+0x+b4HdqD6nwd2j7AbXdJRR6TODjipTTq/1UH3VADK2HIw6Nock3w==[/tex]因此[tex=19.143x1.286]GLuU0t0CE/zQfjVzjfltdXPR3xyalBZ9v43SIO9LMj6wMh2UFtc3bs6mfEcIUOviibhhLNhAcYVSKOHUFgMmuyzzKtQybP1uA7A0mzC3xUgQo/OUiUogAi5ReCEkOdmskgi6TIRnJIg/YzfNj30SGWrQos80vPw+UeoMcNg64tM=[/tex][tex=12.0x1.286]XjskHDE9A6fPyG5P6b2D6QrvoLyFVnXkmjO1J3G4fymn+ZVSN5XqP2UV0qN3Bz7ZrhtF07s/WmiipXEXIReMDE/IBAam1hX7ZLUvmpuXhv/WYXpDO9TRBbFMDDcj0L/a[/tex][tex=13.071x1.286]MDU6wFFbekzuDKmtmnqRi3V4+7r3cfSmOspQKdIrV+4clkYlZTudD+Oi8a898a10IkDVpuDwFO6r8RzOMXH6y8Q5r5wJS2+JaWZnaOUCTThG0mHYjqiGBFa6aidSPCf4r3ZQG4mE1lYCVZneFkk4nw==[/tex][tex=5.214x2.143]cprEwIKEG7K+XfJ+BJWkaVLHNJL/1svTUsZ6IClcnYAPCqrS7GRXbMO+nyePBdb1pmbFAKGmqR8lalIyCELsKQ==[/tex]，于是[tex=2.0x1.357]6D04mYW2ivsCmiBu0E4w8w==[/tex]在[tex=0.929x1.0]mQGdf3XTfQx0Qped0rrM9g==[/tex]处连续，由[tex=4.714x1.357]YbV5C8R7oQk66CznB83eALbNwv6gAKtU/0Y2Y/+sHR4=[/tex]的任取性知[tex=2.0x1.357]6D04mYW2ivsCmiBu0E4w8w==[/tex]在[tex=2.571x1.357]sjdPs/hhXAmvACj9h5RVRw==[/tex]内是连续的。

举一反三

内容

0
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].
1
设函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在区间[tex=2.571x1.357]8LHWfYBWlVDiWkeCm2XuKQ==[/tex]上连续，且[tex=4.857x1.357]59tnZk/MTeLaeqFrBGINZA==[/tex]，证明：在[tex=2.071x1.357]/jRCnEDg+77BnalTVEbF6A==[/tex]上至少存在一点[tex=0.5x1.0]jedlXyMYwmfVwxRj2j9sSw==[/tex]使[tex=5.571x1.357]N0Q796RLZIK4c+sMmxeBaw==[/tex].
2
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?
3
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 。
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]