考察函数[tex=3.071x2.429]ftjKUKqArGhcMEOG3HTbBKKjP0xTv9JQwu9vI+UNuvw=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
解当[tex=16.571x2.786]RhvUqbJHRT3PMHZS3OW6+OEx6LF5maHxkQyOY9YFGaLWNQ9OpsESXkNOuHO3PaHnComToZb8wadcLok73Nx+hf9Iiq5j9MLl8FeUS5qGEKs=[/tex]即[tex=6.786x2.786]p5C2Uh2s66nFM/9B2tJuoiUIe+PWfrSn4tszotPvVssFlI4zcKQTkU6hp49lCsn9[/tex]时,[tex=4.0x2.429]ftjKUKqArGhcMEOG3HTbBMcz7ikKGKHiUl7b/RQ7Whci7HLWGLM9LN26a3t5znT8[/tex]无限大,可见这是函数的极点。由于[tex=17.071x3.714]uZD76Q723fz07zDA0X7gEVzTruGRsGRwbKrQQ/OiKxTqLf8oSe/MYx6f+GYPy+AoZ71VXvVfUy4exX6ZxLVTl0OcHF3SZckfW0W9Qcw8G64N4FwMsQVgo3zvoU1Mgq94P4qvoOxJvdB6mK632A1Gkf65Gkv7cIqu2jfoYt5HnBJ0DK+iuVvwt+3iAtu3tzN8+lfhkwu9M9rhpa0ZXQVsOccAry8aKu0QXpgwZGrbXcU=[/tex][tex=18.5x3.071]Qif26GWhqPUM/Yz2V8uxeC1n+BxyavkDpf1fB3Zmkh4DB4y4rYqBTG3ccx/xcwp7KVPrnla3efXjEnI+38NQ/kpBvrTjndqCEQOO9Z0eVQYeKIzyXjH9HY2piDDKk2SEXXS8AGF4QgQ37ctohhXzMYxeLyChXlWyehL8MdP8ef3LH3y/n85OpeJ7SmWxhrXUpUbeo50tHBxzKXVHm15DFUZpblEmpRlxoI/k/12QcQLt8Z8vyJjRYF6XW8F9SNfr[/tex][tex=1.5x2.786]ZSXg6MFiIkeV34DzbSEb+Mk5sqJS2Kb++LM9ZetbxP4=[/tex]型不定式，可应用罗毕达法则来确定其极限)[tex=23.357x5.571]9vD2uFyUbMyg2IC1pioV9/G3wUCSk9OU+4xbjxf/AREKFC7BjoTiMbwqAP44pe9+GSu6DPYJ1fSMTRn1T53Bkw8QtUrW6UySHMjshtH1TznlaEovMTQTQK8nAqsQAGntE2Ye7Hyw44xDekwLP2qj43NOkKIYc4StzF+ihv3hu6OmKm/JLGaJBbnIh535x3Mp1f5T7NSCRpF5BB3SgOKB7qRfZVMoMeyIjXej+aWzz6enntwf/1L3Vl3+gAfwa+m4LzJroDxO7NZ+eoTcJmzPs0oaCCTTYKswsQkLwEJsfZDi4rBqvCsaoyA1LW67KRzDIvstERKSUa/PyhmiS40Pp/sThVrUn31tr/6Y+sCV6H5/Swr7iKOokHWvC/PSsVzCqfXnNusi2TdO0P+r+aJMAcCMf+rCfZlgEbYtiAiNszM=[/tex][tex=9.857x2.357]ufpcLPj7fW/oL5VBsMHo1gNn3RafxX0qPmf4krGjV7ceD2oKHf8PWwp/DG7fhXf7Eci++CG52A8fhrkDZHNA+UvkSwg14j56RXd9EnSkvsVa4FV8dha8pVw4dgWPg4C2[/tex][tex=19.429x3.071]tQa1PcVlPO8dAT6XQQITTh90pm5TH1mpX5xV5W8aUsINMM2fqdav1a0sDV0rFzwJhXh5NHJeOdeqvjJjPmVroZ6FLBX5Ib/aQnIbMdTzEYUBztSc8hrpZI8b530OxAQ3hy5t8an4DEmgVaCXWwQKrHotWsZsVzxTlZALMT7l1cBk1aVn2COKqrZkkfKSdIazquNp0jL1WLqmlgxSU7g89WqHEA7ow4HuaCEbaUGQw4xVKIl//b70G1lqMuzQ5My2[/tex][tex=8.786x3.571]Vm8eyC5QNdhPWF2I0bYX28r2JJhDaVvA2g7wg7BhEAXGFm1uAl39gLW9B06d4LMLMapBxoSqxSIUQIbk4cGgEg==[/tex]有限值.因此[tex=6.786x2.786]p5C2Uh2s66nFM/9B2tJuoiUIe+PWfrSn4tszotPvVssFlI4zcKQTkU6hp49lCsn9[/tex]为函数的一阶极点.[tex=1.786x1.0]5KB+jUnt4Otf5O87DVSdKg==[/tex]是函数的非孤立奇点。
举一反三
- 考察函数[tex=1.929x1.429]ftjKUKqArGhcMEOG3HTbBFI1EXZpXLus6r7T9AaMgCU=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
- 考察函数[tex=1.857x1.357]5BmRub+CXMJ3SmmVDJzbfxtuuNPKNSM7BY0DS1C3Nx4=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
- 考察函数[tex=2.429x2.357]HexsexC3m7iKx56EYzyiANweC1Eti9ESBk6FywZPVwk=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
- 考察函数[tex=4.214x2.5]uPFjGZQnABXPROTPlhfqPVZQuqaS7HmvwBdAYO9MseA=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
- 考察函数[tex=2.143x2.357]iqbA/0khDcFEYjXFBFr3HPOOFEE9jdmVdX07Cyo6UEo=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
内容
- 0
考察函数[tex=3.357x2.429]aLhRLwaN7tRgtrN2kRQ92pUclt+/QXX1ZdfUma1hEc0=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
- 1
考察函数[tex=3.714x2.357]A6se9H+UT2+H0LXsIiZC2nbk8mAH/4f+78ugmHI+ShU=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
- 2
考察函数[tex=4.214x2.714]/UOGJqOT8ZbBPCEEYV/OJ09wlIqYZUc0VbFOgB4ibHo=[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
- 3
考察函数[tex=3.857x2.5]ysJ+VQ1d/PFjtuIATUYhcYPX/7xsATP6t/Q0cy+VcvITUXXG/oig2YrHyj8mu2y1[/tex]的孤立奇点，并确定它们的类别(可去奇点、几阶极点、本性奇点);
- 4
指出函数[tex=2.429x2.429]2usJeXtOs9mUMvvMBvLtaKKDN0Ce65JcfJWZQfZmzYg=[/tex]的孤立奇点类别，如果是极点,写出它是几级极点.