设函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=3.429x1.357]Dt2CyVOo2zgCzBMWt8ghpw==[/tex]上两次可微，[tex=3.643x1.357]nJ281dB07Q5u/6jyXxdDXw==[/tex]，[tex=4.0x1.429]G9AWbPlmNZXLrewEKQ/RkA==[/tex]，[tex=3.429x1.357]QLWaxXQe+Vb1dzN3hgLB2ofCP4vyTJN9cim5UPyo3Ho=[/tex]证明方程[tex=3.143x1.357]GaUU+prLnDPZRkTgFIz5aw==[/tex]在[tex=3.571x1.357]AUjXTD9IX/KzM2nb6NL7ng==[/tex]内有且仅有一个实根.
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]
- 设[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.0x1.357]bXp5Vb63IyKXaWMS3BCP6w==[/tex]上二阶可导，且对任意[tex=3.429x1.357]WwD1rvmcLUz5NmrhSa2JkQ==[/tex]，[tex=4.214x1.429]79SmwT+8J9VTqKDgDEyFq1vVHcFaA72erzSksXrlPTQ=[/tex]，[tex=5.571x1.357]tuwRu6EZLCuuzT4wtCfHiA==[/tex].证明：当[tex=3.429x1.357]WwD1rvmcLUz5NmrhSa2JkQ==[/tex]时，[tex=3.714x1.357]mXvJ+AdSx51b9k85jFWYgw==[/tex].
- 设函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在点[tex=1.929x0.786]qBxW1Wco1uHB6W+VkCK3Kw==[/tex]处可导，则函数[tex=2.429x1.357]9cM+yXmMqe9Sxnqa+l2Eqg==[/tex]在点[tex=1.929x0.786]qBxW1Wco1uHB6W+VkCK3Kw==[/tex]处不可导的充分条件是 未知类型：{'options': ['[tex=3.143x1.357]E5AUvOOYCnpTRWX493K7fQ==[/tex]，且[tex=3.429x1.429]juhGKpKYVWMENuClDrEvp8Hrkq74GfhG1bVrRi5KhxY=[/tex]', '[tex=3.143x1.357]E5AUvOOYCnpTRWX493K7fQ==[/tex]，且[tex=4.0x1.429]B9nTa3QuDTLw/pSatPVGiNexWqYcOJXHovv8ZtWKMnc=[/tex]', '[tex=3.643x1.357]7ialSGgtd2YgqZew1RQd0w==[/tex]，且[tex=4.0x1.429]gvhP1AY7iQv59UiRiUjPvvU+eSzVq48eXIp057thEn8=[/tex]', '[tex=3.643x1.357]tOuVFRflAteCgvb7gGHBlA==[/tex]，且[tex=4.0x1.429]Lp8KhkNyKz5e0lhVFUWU01qbIQX0AoEACKUhayeOBkE=[/tex]'], 'type': 102}
- 求函数[tex=3.286x1.429]kdT+eIE7CHPynuN6CaN40g==[/tex]（抛物线）隐函数的导数[tex=1.071x1.429]BUw1BPFU3fsJlAl/vt9M9w==[/tex]当x=2与y=4及当x=2与y=0时,[tex=0.786x1.357]Hq6bf3CacUy07X+VImUMaA==[/tex]等于什么?