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单选题 二元函数的极限存在是其连续的()
学科：默认课程
时间：2026-05-10 10:43:03
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题目1单选题
二元函数<img src="https://tihai-oss-cloud.itihey.com/img/966884ca91d6f73fe1ac76259b7fc510.png">在点<img src="https://tihai-oss-cloud.itihey.com/img/d733a10e667d402bd6375b5d225f5f72.png">处的极限存在是指当点<img src="https://tihai-oss-cloud.itihey.com/img/4a7e584bc7510c64a8d84995ec821b50.png">以什么方式趋近于<img src="https://tihai-oss-cloud.itihey.com/img/d733a10e667d402bd6375b5d225f5f72.png">时,函数值都趋近于同一常数A. 任意B. 特定C. 直线D. 曲线
题目2单选题
若点<img src="https://tihai-oss-cloud.itihey.com/img/7b9c8b5707564b2c09ab8b55c4ba0832.png">的任一邻域内既有属于集合<img src="https://tihai-oss-cloud.itihey.com/img/fd228fbef8631e93241ad6c277a8164d.png">的点,又有不属于<img src="https://tihai-oss-cloud.itihey.com/img/fd228fbef8631e93241ad6c277a8164d.png">的点,则<img src="https://tihai-oss-cloud.itihey.com/img/7b9c8b5707564b2c09ab8b55c4ba0832.png">是<img src="https://tihai-oss-cloud.itihey.com/img/fd228fbef8631e93241ad6c277a8164d.png">的A. 边界点B. 内点C. 外点D. 聚点
题目3单选题
二元函数<img src="https://tihai-oss-cloud.itihey.com/img/81484cfb497e84eebcb4814968198dc5.png">在点<img src="https://tihai-oss-cloud.itihey.com/img/d733a10e667d402bd6375b5d225f5f72.png">处连续的定义是()A. <img src="https://tihai-oss-cloud.itihey.com/img/2eaca92f7196b29690b3c3bc52291a83.png">存在B. <img src="https://tihai-oss-cloud.itihey.com/img/5546964ae73cc7ca77e698ccaea41a28.png">存在C. <img src="https://tihai-oss-cloud.itihey.com/img/0c97982130423db2d1159696278251ef.png">D. 偏导数存在
题目4单选题
二元函数的极限存在是其连续的()A. 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件
题目5单选题
函数<img src="https://tihai-oss-cloud.itihey.com/img/0b4802a99ae97de898f0c4b60b685cc7.png">(<img src="https://tihai-oss-cloud.itihey.com/img/3779c53dfa0fa2efb2767e45647d5357.png">)在<img src="https://tihai-oss-cloud.itihey.com/img/361f803fede7a7a065681a081d6e7596.png">处补充定义<img src="https://tihai-oss-cloud.itihey.com/img/1aed8f73b00866b024fc698ad31189c2.png">后连续,则<img src="https://tihai-oss-cloud.itihey.com/img/58ab56424a322b3886da0480aa236605.png">的值为()A. 0B. 1C. -1D. 2
题目6单选题
函数<img src="https://tihai-oss-cloud.itihey.com/img/3c9b20a40fe56c7e344b8810ef891cba.png">的定义域是( )A. <img src="https://tihai-oss-cloud.itihey.com/img/6e14eb419187ff32e0e1ef9160c562aa.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/774eece6281f740a7ad93a4f35552e5a.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/de9399739527d4563f5fec9909a3f7b2.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/33149896f3339b3132d04470c2c54cc3.png">
题目7单选题
函数<img src="https://tihai-oss-cloud.itihey.com/img/96bb827c2e1e5497d195f37053e0be97.png">在点(0,0)处( )A. 连续B. 极限存在但不连续C. 极限不存在D. 无法判断
题目8单选题
函数 <img src="https://tihai-oss-cloud.itihey.com/img/e574bf484288b6e3553eb03d49827602.png"> 在点 <img src="https://tihai-oss-cloud.itihey.com/img/d38655c020069270af9fd0d633bb6ca8.png"> 处对 <img src="https://tihai-oss-cloud.itihey.com/img/d73e6541f76b20966ae90787ce71cecb.png"> 的偏导数是( )A. 2B. 4C. 1D. 3
题目9单选题
设 <img src="https://tihai-oss-cloud.itihey.com/img/e054fef7f28f3fba872ee729be23361e.png">(x>0),则 <img src="https://tihai-oss-cloud.itihey.com/img/ba0ff4ce6a56d6371dd3cc63a4b59b83.png"> 等于( )A. <img src="https://tihai-oss-cloud.itihey.com/img/c935bcae527d182507d7fd32912cf281.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/68f5d71b97bde71b11dd7f3380b9e469.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/3b3c922a32f1695ec49933d4768ec30f.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/2545bb4b08849af1cbe77444f3b4b40e.png">
题目10单选题
设 <img src="https://tihai-oss-cloud.itihey.com/img/6bac60250b7562ee5e7e210b1fef5dd0.png">,则 <img src="https://tihai-oss-cloud.itihey.com/img/ba0ff4ce6a56d6371dd3cc63a4b59b83.png"> 等于( )A. <img src="https://tihai-oss-cloud.itihey.com/img/ef1aeffa08b886321dc1a4deaa76cfe2.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/6802e68c3748a5306787960bd5a279a8.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/e551b46f4322e73ec76a837c00b53f09.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/052d30c1fc6a8b9237c2c53efaf376ed.png">
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