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四种方法证明0.99…=1，从小学数学到戴德金定理
高等数学合集8/44
![无穷小量和无穷大量的定义和关系[高等数学7]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2019113d8d084736a6eebda58959f085~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=Qu1CNc6yvgo4FYRd74jWMk9mhl4%3D)
App20:50
App11:04![无穷小量的比较[高等数学8]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/ef7f3c4d69e34c7581d228bb2a4a18b8~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=dX4CL%2FguDPksQ3isLsgycR0s7tQ%3D)
App15:44![连续函数与间断点[高等数学9]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/720bcd92ad6a41ea8b5c8dbc2ce2b7b3~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=TAkOyyLYj9vHmw1xtBmjX1plY5I%3D)
App25:12![[高等数学12]反函数、隐函数、参数方程求导法则](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/e18118dc9b9e457980b77f4b0237f812~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=fUBWiv0A8vfiror1JRC92zpKxOA%3D)
App22:36![[高等数学11]导函数的概念＆基本初等函数导数公式证明](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/cdc442e692724b83b411ec1f0fdc36a5~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=pdk6m3LYjii%2By6yKuGkh2dBjlDA%3D)
App21:41![[高等数学13]如何理解微分？](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/a2e0de967ce7448db9f799b79ec8bd6c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=f85fdRJ1yXqyrrpW105DsAnBstU%3D)
App20:26![[高等数学14]罗尔中值定理——微分中值定理1](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/0dd23ce323604df4a87c0667566d4e2d~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=zllmzAWZPXiGjtrUo5Lomyipf80%3D)
App15:41![拉格朗日中值定理[高等数学15]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/3a98032c3fb24c2d99861489d679f061~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=hQ0B0lC8V8G6FPEEwuiv%2FuICsmA%3D)
App20:47![[高等数学16]柯西中值定理](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/f5d1aed39d4f4b369461c2e9aa6e7395~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=1Gmo0NEsZsBrIFCKek5aF8W31zs%3D)
App11:23![洛必达法则[高等数学17]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/02cb1d84c0fc4ac68f45fc5bc2ac2b5f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=Ws1qZVSGqyBGl%2B%2BiYzbZKBmRh5Y%3D)
App21:09![泰勒公式及麦克劳林公式[高等数学18]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/4960df96913d4e95827aea2c843d5168~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=rZ4TfikdbB80tEOPoT6cH42B2mY%3D)
App15:24![泰勒公式的正确打开方式[高等数学19]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/2359e6b0942345a89a6297704294549f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=A0XwzUSQsIpZrzt3Bp8cpUkkFbE%3D)
App10:09![函数的凹凸性[高等数学20]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2bccdf5604834d139776bd5cd6d0b198~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=YSbgJZExK3JiRAcRFGSDemaAmqg%3D)
App14:58![不定积分[高等数学21]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2d430c39d9c54b4483d0eefb2d092179~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=eenQ3CqOyanvl4J9crcH5hmvUcw%3D)
App18:06![换元积分法，第一换元法＆第二换元法[高等数学22]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/b7afa697793c4b1282bea0e02a6e9930~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=MYEdIAFRqwRAMseEny%2FtYxRg%2BD0%3D)
App15:13![分部积分法[高等数学23]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/083f53d7b0ae43b8847f19fcbc9f394f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=4Ufg5DV%2BqGbQfCGBfpKadlm4YlA%3D)
App08:57![什么是定积分[高等数学24]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/5c8c71b363564ed2aa57b045bd5b14e2~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=Deh%2BwfjI1QWHB7%2FouI%2FIMkYIEy8%3D)
App21:43![积分中值定理[高等数学25]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/1f9e13e0921f4c03bf4bbe52c72ec65f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=xuuM9nxW2M4AZz7C7yia1i%2B2eyQ%3D)
App09:52
App17:38![定积分的换元法[高等数学26]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/98c772e478714761bfca2c4d1a97cfc7~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=cGYzKBcHjNmvfLjB2RcxG%2Bj6bHM%3D)
App17:15![[高数下册1]向量的数量积，向量积，混合积](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/8fafc85116c643d18a12234272a6792a~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=BG5kIMlj%2BiYV7uxfG%2F4WQeBwN6A%3D)
App27:30![[高数下册2]空间中的平面方程和直线方程](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/641e4a6b0bc44a25a5da0481ec6c96d6~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=jY08roC1YGv70%2BfwdiHJrbSHbKY%3D)
App23:02![多元函数的极限与连续性[高数下册3]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/43b3473bad6449f2a2f177d94181ee75~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=1HfNmdh4balxENaZki5XazfVLXM%3D)
App28:00![偏导数与高阶偏导数[高数下册4]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/cce162b9643d469e979ffcc8862ee3db~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=PlUO07axaZDUmwHy9xxYZe5hMuE%3D)
App21:47![多元函数的全微分[高数下册5]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/60639dde2fdb4ab298fc863b87ccd03d~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=ec0K0FtA%2BXDDa2trKGWnS0tjRPI%3D)
App25:42![多元复合函数求导法则[高数下册6]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/13b47be6747348bd9c3f3a8d3c0abf29~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=gdHsfcPFfSG7EmpvNm1jW8s%2F%2Bes%3D)
App22:45![多元函数隐函数求导法则与Jacobi行列式[高数下册7]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/bc62f6d364304761bfc983efb3b8a5df~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=yPuvjdArrwa%2B5GgtotZEMJzaJzA%3D)
App19:18![方向导数与梯度[高数下册8]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/42dd554276584ebe95cf050b8b5d69cb~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=kKYBjatGbXRvVup9jPoV%2Fm2BcT4%3D)
App17:25![二重积分的概念与性质[高数下册9]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/7920905eba7b41ff97ca8de77ac1721d~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=I%2BkJ0R5%2BldO99Xma7gp0r0qAq2s%3D)
App17:03![二重积分计算法——直角坐标系计算法[高等数学10]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/0c14b406ffd641d384d4a75dff0fada6~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024111113464633F6431243C8E3774E3B&requestFrom=704&version_code=80402&x-expires=1762840007&x-signature=4eXbFNAJUTuyOS%2FXWYVi3KOtOCs%3D)
App13:12打开App观看
