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[高数155]求极限|利用Taylor公式求极限
高等数学习题讲解 第155题
高等数学(上)习题集137/264
![[高数154]求极限|抽象函数的极限问题|洛必达法则+微分中值定理](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/849eb0a500fc4c6380b30dd9b4e0f6c3~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=HdLrh%2FR2Z4kn4OZZPdLmFg0wKQo%3D)
App07:18![[高数155]求极限|利用Taylor公式求极限](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/cd0bd55c4d87413e9d184e3079166694~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=QQJFyoXbHW2CJ7HD9v%2FGgkwYNz8%3D)
App08:49![[高数156]求极限问题|利用Taylor公式求极限(2)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/98b404e2f7f1445893bbecb05bfe681d~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=aLRzC%2Ba0xOa2TfG6QBQbx1XCT6o%3D)
App05:56![[高数157]求极限问题|利用Taylor公式求极限(3)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/fb0283b451834da1b9c47bfda4440861~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=6NJTIs1%2F51fIYSwmRLFYhWHf%2FFo%3D)
App05:04![[高数158]求极限问题|利用定积分的定义(1)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/2f6e428f68e24585a7da00dfdca6b1c7~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=ha5Ue153iwwJQVAlXsvXy3Z206o%3D)
App05:27![[高数159]求极限问题|利用定积分的定义(2)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/dc1310def2a0443fafb523f9aaf41976~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=oyKAKH0ZWUXRIdowJ7GMSTTB0iU%3D)
App04:55![[高数160]求极限问题|利用定积分的定义+两边夹准则](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/f96cf433f4544601b0151dfae40065de~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=qJZ9CV9Cx80S30BW%2BitVAkEd2A0%3D)
App05:55![[高数161]一道利用不定积分求函数表达式的题目](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/bd66185e4f5e400d81d79608a7a06c09~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=TlPRaGLCT%2FwBS%2FZXbWsNmcHaOIE%3D)
App07:13![[高数162]被积函数是分段函数的不定积分问题](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/36c2dcd42eb54ed6b3947e1e3cb82a71~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=2GXEGTU%2Bq026jjQxNyo0cIBf7%2Bw%3D)
App04:09![[高数163]被积函数带绝对值的不定积分问题](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/1e7bd3e72231482eb40ce7bc023a884c~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=FdbiMJaLSJTZaJKD8mg5YpaQ7lw%3D)
App03:49![[高数164]隐函数的不定积分问题(1)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/16d57214be694c16b18ddcb17ab232b5~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=zQfX8ryr%2By1TtFf9sfm7l0nXBwA%3D)
App04:54![[高数165]隐函数的不定积分问题(2)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/bfeb34fd42b245c2b43bf283fabaac14~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=MIdMjahPp3UYYbVlYvHkRILe0Jo%3D)
App04:31![[高数166]未知函数的不定积分](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/ddd321a2c39a446cb223b4153af9aa4a~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=WjiDubQoBSQfNMcXjJ9iSoSXzR0%3D)
App03:09![[高数167]这种凑微分的方法也是少见](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/6420bd1330fd4bb280024435e2b370ab~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=N%2FgrirJtjQzHSak5Xy3qAyg2CLE%3D)
App04:48![[高数168]有道不难但复杂的题](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/94e15bf1e7884823982cd17080a8ec4b~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=i4Ssfhx%2BWyOpg%2BmkiZ%2F1NVa%2BzPg%3D)
App08:08![[高数169]先倒代换后根式代换](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/76d32cdc203244d4bfe117ab240d0cf6~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=O%2BR%2B2b2rf9w75zVVY2GMyy5E6HE%3D)
App07:09![[高数170]题目简洁但解答过程复杂](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/0e5398a781cf4715ae99c4bdb49de1b2~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=tHgx5gntUJJ1uUTvFJVhgBvo0so%3D)
App11:20![[高数171]注意观察被积函数的特点](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8376261b53c44289aa4bb0bbf724d157~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=v2tqjrCSUWupRGx5%2ByGwbGz%2F9K0%3D)
App02:39![[高数172]见招拆招|遇水搭桥|逢山开路](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8afdf78dcc004f0686158fab4374e3b1~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=5z1RG%2F07ygXmBajqHqwNGCrBQtE%3D)
App05:34![[高数173]这样子的被积函数可以使用根式代换](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/9c1d68c58ab84829834200c0a438e2aa~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=BRomeDlXUGu8pnq%2FsZwcb3zU6Kk%3D)
App08:42![[高数174]三角函数的不定积分|三角公式很重要 (1)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/008446c617d34ec7a4c7a1e5055448e0~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=2VemQQ2D9UUpoalcU19iO98VU1k%3D)
App02:20![[高数175]三角函数的不定积分|三角公式很重要 (2)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/5af14b80a1114bb4a196fdc8d4aba75d~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=0d4EmV8HS1Bb4T1%2B23iulX5Y7LU%3D)
App01:57![[高数176]三角函数的不定积分|三角公式很重要 (3)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/07dde814583b433bbfcd623611082387~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=CXiUThkvyJWtrC9BcBp8S%2BKmx6k%3D)
App03:06![[高数177]三角函数的不定积分|三角公式很重要 (4)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/6c2323be51094d69b65c6573a83c6e33~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=dh4VFoeqXQAUmXDXswlOmWYttW4%3D)
App04:16![[高数178]三角函数的不定积分|三角公式很重要 (5)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/7299bb1d65a147968201d509883b6d4e~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=MuiUI0n%2BJbWiswM1n0GmFcwiQZQ%3D)
App05:22![[高数179]三角函数的不定积分|三角公式很重要 (6)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/0921484550ba48ba980761c07fa2861b~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=5ZJ6BPX0E8iTPuyNC0q1YGASrEg%3D)
App04:38![[高数180]不看答案我得想很久](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/c54177f0ac484b668b99c9704c9d92b6~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=20241106111538A12F70FDA8C43D5CAFEE&requestFrom=704&version_code=80402&x-expires=1762398940&x-signature=9PX03A55IdCPOXR1iMrdNR1ZFlo%3D)
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