证明函数[tex=4.143x1.429]cEFDD/xbaqLWp+KOUfAvxQDFG2tl9yHNqmfKORRcrPM=[/tex] 处处连续,但在点[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]处不可导.

2022-06-19

证明函数[tex=4.143x1.429]cEFDD/xbaqLWp+KOUfAvxQDFG2tl9yHNqmfKORRcrPM=[/tex] 处处连续,但在点[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]处不可导.

答案：

解 设[tex=2.786x1.214]t4PQMe6S7lgnx4jkn9z6Og==[/tex], 且[tex=4.5x1.214]sjhYfqRFIpUQ326y8qJ8WGbC3Cx+VIaGH6+drz6eGx4=[/tex],则[tex=32.571x12.643]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[/tex]这里[tex=2.786x1.214]t4PQMe6S7lgnx4jkn9z6Og==[/tex]是任意的. 当[tex=2.786x1.214]lPAnD3S8gHy8zaNIUmXxTQ==[/tex]时,上面的极限不存在,也就是[tex=20.143x3.071]j7nOhXvwRASzuk3Za/to8H2/M4w0RUUprhxYjqoVBO74xbvvklw266DsrwfH2pNmyS9IlUTxnW9Z4ygyNktCN7qnjfpwxUO9KP7oOcIiPo26DytAg7GAttIcBbWaKbwbYMf0vj59LvGfAdWKouzRdcdYTm33Tje4jUWH9pvaaq4Bnwrh29f9jFJ6gzzd3zfgeCd9k1u0+ScbDaz5FfqtDTVIGa6jbRDBEGLFH4BrtgvgUlVJXgJF+5kOErqv39fGKWOKw8Zzs2TYYqVM8ilH3g==[/tex][tex=3.643x1.286]eJogY9JDx/NBGBjYH2IfUK5h2i9w35DrSeihjqmt2I4=[/tex]所以, [tex=2.214x1.429]8cd96CjdKQybv+xwHUVQpw==[/tex]不存在, [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]处不可导.

举一反三

内容

0
讨论函数 [tex=5.429x1.286]L5oXdXwgxkTumjSWejhUP5DaSa0qAduchGfzRS2ajZE=[/tex] 在点 [tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex] 处的可导性,若可导,给出 [tex=2.429x1.429]TwuB3PkohxChlun8klMMAvduWoHFKGC+hQUkdVpehqk=[/tex]
1
设[tex=1.857x1.357]fBOYuAIZ/H4m1Dx+my86tg==[/tex]在[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]处连续，求[tex=7.143x1.357]WBHzx45u9p6ikQbcvJXksk+/jCvyYca+kc9mrxy+h0o=[/tex]在[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]处的导数[tex=2.143x1.429]cyTLS33m58hKP2tqKCic2g==[/tex] .
2
[tex=4.786x1.643]DU0rUnWXsXr0JAG1m3XeaAn37ASrg2xrNPV3iioolmI=[/tex] 在[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex] 处的导数为______,在 [tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex] 处取得极______值.
3
设函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=1.857x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]点连续，且极限[tex=6.429x2.5]ENxIatiC2yqgaopSQCG83t3kurVWrMzpBRbeYcnuiQ8Lr1QVkHWb83+M9PWElMGa[/tex]。问：函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=1.857x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]点处是否可导？若可导，求[tex=2.143x1.429]mzwRhuDvrCMocO2CEffeaJzsyOyV9IHxECuGvFss+GU=[/tex]。
4
讨论函数 [tex=3.0x1.357]37/oZRunQe/zDscJjjjR3A==[/tex] 在 [tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex] 处的可导性.