• 2022-06-09
    设连续函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 满足 [tex=10.071x2.643]BbdvBXivohKVDCYgD0y1dswEnw9Dkjneq8D5uIWI4k61zg2QJ4lI3CGN71EMsKz/[/tex], 求 [tex=4.786x2.643]NYsWooW1AFb3nEYYUOvAHtK0CdtL0HiryTvkddsLuEKXEe1O/TjbiGJiQQdBQf7t[/tex]和 [tex=2.143x1.357]BazjA76tgLiCVqPsTb0axw==[/tex]
  • 解  令 [tex=6.286x2.643]NYsWooW1AFb3nEYYUOvAHhmMhIwf3Mp43WJwjyATJgMBaCdlC/fD4QNwQRP1fBBK[/tex], 则[tex=6.214x1.357]yU0Bc6uo9KMVxoCbaMtogw==[/tex]两边从 1 到 [tex=0.5x0.786]X0W0/ANSf45taW8iXDx3lw==[/tex] 进行积分,得[tex=25.571x2.643]79c6MkgVQB4xvZ4Z3ydRxc31xbYPkGLWFq/x85PEL8DvZlo76rgc0/cpolTRL9LBbGEdiaNjJlQgps8vKfwKjcO0vPoHJ7yMVhqQKrgyGsvty5mHTkcbe+wGITwXJg8t5WC3F7a1qlyDe60COgyrjJsFkI78r3H2re1Q7eZIzA59USHvsitzRzooBcj6MspIi9lrkZ8puuDpZFTHGj/dHg==[/tex]于是[tex=14.786x2.357]cEJ2zOErJVuNxHL6zHR8Jnej3aVazjEWScTL4YjguSH5D3S7wXvHaqUsiFUuQmmLAPZ9D7iRVSQ19+Lyb9EpJzpctG9HxSYFg6bdtEeK74ffvYQYxSeiWK0aThJ1fT74[/tex]则[tex=7.714x2.643]79c6MkgVQB4xvZ4Z3ydRxc31xbYPkGLWFq/x85PEL8BqDUhRuA2LTvkMeJNlsxR5WXz+unvtzXQNn8Z1Tqu993rwEAgUprXawr0j8Xo1agU=[/tex]从而 [tex=6.071x2.357]WzPKNBZpJfdxgbEvaDBMumiDtPxbgVhJho3tVnCeL2fy0wEmbYqyFihP6AvAT/l3[/tex].
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    • 0

      设[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.0x1.357]bXp5Vb63IyKXaWMS3BCP6w==[/tex]上有2阶连续导数,且满足方程 [tex=10.714x1.5]79SmwT+8J9VTqKDgDEyFq53sXv8i7JEFdpsaW068Ose09yUYGhX1v6tjCCNywn3QNHpR1XTDhLUiT7SyEWJ5lw==[/tex],证明:若[tex=5.571x1.357]fZPOLhn8pxWflc83qanxJA==[/tex],则[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.0x1.357]uQo0Qwms4Bgi6pleNWBbfw==[/tex]上恒为0。

    • 1

      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?

    • 2

      [1990 年 1,2] 设函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]连续,[tex=7.929x2.857]BsuvG5KmQSYL0mWCagnBwpACpIm6SKiwHUxiqa6OIucmsIEju4FmgYIwoQj7L/YK[/tex],求[tex=2.429x1.429]aXb7OX6mdt0EhzAzoeML7g==[/tex]。

    • 3

      设[tex=9.0x2.857]dT5tO8+kvspSX29znp6hWPcRleyC/Oor3hOtFnEeVKWMhAwyQN1L849Sg2m7O8+O[/tex].(1)证明[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]是以[tex=0.571x0.786]l57IXZOdm4C+U7oqJ3rVIQ==[/tex]为周期的周期函数;(2)求函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]的值域.

    • 4

      设二维离散随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]的可能值为(0, 0),(−1, 1),(−1, 2),(1, 0),且取这些值的概率依次为1/6, 1/3, 1/12, 5/12,试求[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]与[tex=0.643x1.0]O+viFNA0oHTwnBtQyi80Zw==[/tex] 各自的边际分布列.