设[tex=2.786x1.357]eWdlhSDnEKsnC2m9ymU17w==[/tex]是可微函数，且[tex=10.643x1.5]sUEvI5iPbIii0CJB/fO6yZVF8UJWPeUv0wmUnjU7G9t8nnyMDVn/vAfdIvsKXBia[/tex]，则[tex=4.5x1.357]b+vw7vXgaNRHisZpcPW1Rz28EH97pfEAPJRqQIECAnA=[/tex][u] [/u]
举一反三
- 若:(1)函数 f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数;(2)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]有导数;(3)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数及函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数,则函数[tex=5.643x1.357]GmtX7Vop79exGU/rpqXUYw==[/tex]在已知点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]的可微性怎样?
- 判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]
- 试证明下列命题：设 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 是定义在 [tex=1.214x1.214]u/EwPhudbQnOqlmqWT4jSQ==[/tex] 上的可微函数,且[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 与 [tex=2.214x1.429]8cd96CjdKQybv+xwHUVQpw==[/tex] 都是 [tex=1.214x1.214]u/EwPhudbQnOqlmqWT4jSQ==[/tex] 上的可积函数. 则 [tex=6.357x2.643]e+yUMNjQeuJYe6l0ZbTv1Ac8pcZ39z+1PFRGk+eBO/dyNHsguj/HLEgcxVLppISs[/tex].
- 设函数 [tex=11.571x1.357]4z5pgOZshJqp9q6TFGtfVCSUy5vK5K2ZA+wyggXFF4M=[/tex] 则[tex=2.929x1.429]j0dbOmFELnxE2KqwRwAMrw==[/tex][u] [/u];[tex=3.143x1.929]PZ9UVo4zsmEWodBI81rRwUGUDXpCN1qk8D6ITWRcrVs=[/tex][u] [/u][br][/br]
- 【1997】设[tex=6.071x1.571]6u/PVhSrPl3hUbvSwBp2oKZLs7n/hP5yxorLGbdaGXg=[/tex]，其中[tex=0.5x1.214]++gGGJQcubEKWlse37f6tQ==[/tex]可微，则[tex=1.071x1.214]6svmbb+oZ3Rd91HR5OCBgA==[/tex][u] [/u]