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[高等数学3]函数的极限
高等数学合集3/44
![[高等数学2]数列的极限，论0.999…=1](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2d41c1942c034ff9be3cc90ece812177~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=aWjsw0vmlXJhYQzQtcS%2BkHIYopA%3D)
App19:33![[高等数学3]函数的极限](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/6f766fa37d3441da9fa09bba0b2ebbda~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=IylcmuGJcvjJhmSXywTqLoNd9ZI%3D)
App34:57![[高等数学4]极限的运算法则](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/dc090c4b9cf74a08a48ba0a30a4ee992~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=AYawPZPG7RovDfJoH967%2BK8RoMo%3D)
App13:31![夹逼定理，如此简单！[高等数学5]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/448df59defba4276b5fcdfcc5afde8c4~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=styIc0ncwDHc3G5dzOpfYGBVuJ0%3D)
App12:03![夹逼定理证明重要极限[高等数学6]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/b41b051513fb4607938416bce9ec900d~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=bizYyWt0dlBDFGSrJrb62GzpOtk%3D)
App14:43![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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=YRrwSTVx62kbzRFkMnnnScUvOuQ%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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=l87JbFTaQ%2F%2BhsMl9NyUxivZxixk%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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=XC%2F%2BzNHA9%2F2LoxX4XHVVvZ9ylzo%3D)
App25:12![[高等数学12]反函数、隐函数、参数方程求导法则](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/e18118dc9b9e457980b77f4b0237f812~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=%2BHFGuTrGDcJE2gAidPs12N%2FWF60%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://p26-sign.bdxiguaimg.com/tos-cn-i-0004/cdc442e692724b83b411ec1f0fdc36a5~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=%2B0d6Xr9ccHc8BV4Jkaus0oKxibM%3D)
App21:41![[高等数学13]如何理解微分？](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/a2e0de967ce7448db9f799b79ec8bd6c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=ZPDQovJkBYwLJMWkjS6o8mgsB8E%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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=HAnnr3%2BB9xtbC7qsZ0cpXLTAhXQ%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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=jfTdGILUmfZLAWlUWZiUTvucmNM%3D)
App20:47![[高等数学16]柯西中值定理](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/f5d1aed39d4f4b369461c2e9aa6e7395~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=bSfv6L0wzR2tiq8gAjAPGulrrP8%3D)
App11:23![洛必达法则[高等数学17]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/02cb1d84c0fc4ac68f45fc5bc2ac2b5f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=mWGJEZU%2FBMi%2F0PZBnpjRzu5lcVQ%3D)
App21:09![泰勒公式及麦克劳林公式[高等数学18]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/4960df96913d4e95827aea2c843d5168~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=MwDz7ne%2Bpkzuun9FSJyGowTW7jU%3D)
App15:24![泰勒公式的正确打开方式[高等数学19]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2359e6b0942345a89a6297704294549f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=X69eDPrdL1Fe9XrlG3snUbUaESQ%3D)
App10:09![函数的凹凸性[高等数学20]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/2bccdf5604834d139776bd5cd6d0b198~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=yeQ574YiRZZQk7ubYY807bvoYNU%3D)
App14:58![不定积分[高等数学21]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/2d430c39d9c54b4483d0eefb2d092179~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=SJLfuzXM5v8vqbFPibFzF11QhMg%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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=W9rkjaRtHcr%2FuGHa%2Fww5IzMT84w%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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=sx%2FlUoFViamC2KOk%2Fen9D1cUAow%3D)
App08:57![什么是定积分[高等数学24]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/5c8c71b363564ed2aa57b045bd5b14e2~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=Ky7QWVPXXjWAThCH0%2FYgTWgSERc%3D)
App21:43![积分中值定理[高等数学25]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/1f9e13e0921f4c03bf4bbe52c72ec65f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=jnlVQ8as1xwsrj5RJEekOTSJQG0%3D)
App09:52
App17:38![定积分的换元法[高等数学26]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/98c772e478714761bfca2c4d1a97cfc7~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=tApj%2Br92Ax9tybt%2BqWjXZwX306E%3D)
App17:15![[高数下册1]向量的数量积，向量积，混合积](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8fafc85116c643d18a12234272a6792a~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=wGeXbYSrVLL0IycjKvPEVSXwZvE%3D)
App27:30![[高数下册2]空间中的平面方程和直线方程](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/641e4a6b0bc44a25a5da0481ec6c96d6~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=WONNamNIrR4z4C8lRCIT7DOIIZY%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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=sRtprTbixOmKseY%2FF0%2Bul6VdbnQ%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&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=yhBx75NuYNBxUks5FZcx9zegUKo%3D)
App21:47![多元函数的全微分[高数下册5]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/60639dde2fdb4ab298fc863b87ccd03d~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20241216084822DC4F9DDB11FC38D6D30D&requestFrom=704&version_code=80402&x-expires=1765846103&x-signature=K%2BLLtp2LWddsz4kBZoErRKhqutI%3D)
App25:42打开App观看
