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[高数160]求极限问题|利用定积分的定义+两边夹准则
高等数学习题讲解 第160题
高等数学(上)习题集142/264
![[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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=57yUodBDM5M%2FDgwZxjM%2FeraivUI%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=ZOgFQ%2BQj4FNbaSJXrWnzkaCWIds%3D)
App05:55![[高数161]一道利用不定积分求函数表达式的题目](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/bd66185e4f5e400d81d79608a7a06c09~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=X%2FHaRIHKpfpvQnMBOENHpqILxgM%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=LT7UNFyK4dJ%2BCvL4gmEqgE3LetM%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=5eAwOeQnEIaPM8FsXve2oUDwTc8%3D)
App03:49![[高数164]隐函数的不定积分问题(1)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/16d57214be694c16b18ddcb17ab232b5~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=tGYEgZ%2BnzAKh0%2BcUYSjUaMz7EG4%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=wRdjjUNCy3TuORQI4FFIb3FcsD0%3D)
App04:31![[高数166]未知函数的不定积分](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/ddd321a2c39a446cb223b4153af9aa4a~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=9kUJQVzdcSCHd7QYPBXxRo8B4Cg%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=if0y5qDqfn%2FpxRjh2l7AwQC247g%3D)
App04:48![[高数168]有道不难但复杂的题](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/94e15bf1e7884823982cd17080a8ec4b~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=F9wEN9NWaAxzNxg9D75nEdZnSDQ%3D)
App08:08![[高数169]先倒代换后根式代换](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/76d32cdc203244d4bfe117ab240d0cf6~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=pjr6qHenO%2B29mrHbGYXAJJTNgpI%3D)
App07:09![[高数170]题目简洁但解答过程复杂](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/0e5398a781cf4715ae99c4bdb49de1b2~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=QsPDZnV2fPwFZ6lCG9BBAKKDSyg%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=PQfGDjPUCpxRHKQK6U5x%2FQfqB%2F4%3D)
App02:39![[高数172]见招拆招|遇水搭桥|逢山开路](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/8afdf78dcc004f0686158fab4374e3b1~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=cR01eUd5PbmVSb4Yd8%2BBscTTJ78%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=jrGodbqhH9ypVNVtFJ6sxwZJggo%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=WWLpypsyrt6CoyQxjs4uH3sDWI8%3D)
App02:20![[高数175]三角函数的不定积分|三角公式很重要 (2)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/5af14b80a1114bb4a196fdc8d4aba75d~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=weDTYfYrTp90PsY1sECmUmC2PMc%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=QIu4EmyJuoe9SlIEAepk5b5T0R8%3D)
App03:06![[高数177]三角函数的不定积分|三角公式很重要 (4)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/6c2323be51094d69b65c6573a83c6e33~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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=Yy1SPfjmNVicTQ2wNv3kChrtXNw%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=zqOIQFoK8qZN15QkTnRwiFOvMfc%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=e3zHPqEeoptbaB5cafo7g6W3sUs%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&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=20250309223922BE672EAF564A91B9BB90&requestFrom=704&version_code=80402&x-expires=1773067163&x-signature=1zu5iC31UNNJfcDzlrCfAt2WHng%3D)
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