• 2022-06-30
    当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时,反常积分[tex=6.071x2.429]QDF3on418hztfquUcJypQYwtonQ+mFtQedEGxyAzTPBBJauFsgD+wTUcaYY8YVBM7TsP3lo1GIiuciBXniPdXw==[/tex]收敛?当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时,这反常积分发散?又当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时,这反常积分取得最小值?
  • 解  当[tex=2.286x1.286]6T11TlvSr5csjeOcKvNqDw==[/tex]时,[tex=28.286x2.571]p0+OH7YNKfNLWlS8e6PskqZQmy0CrtEDRr2Ogwzcej4YxYTcsx8U7OF9w/wKb/JqD+L/obUGaKE5/wWb3mDNmjtLlfQ9oaohBUIi7abJNCPXkYiMtEsVJVx18KVFDm/fLRkeVKbxx0Z7fDFWNkfSaaua31jASxLQsDMBCmgWSqloVw8qwbk57BXSFMuitGPO/Sc1h/l0iQjbFL+eV8k0qg4GN2skwt03CXFcXVGsZms=[/tex]当[tex=2.286x1.286]eURRLN0azYBNN+Lh6BrAUw==[/tex]时,[tex=23.286x2.429]p0+OH7YNKfNLWlS8e6PskqZQmy0CrtEDRr2Ogwzcej4YxYTcsx8U7OF9w/wKb/JqD+L/obUGaKE5/wWb3mDNmowwJrswCI2doYR4ycb6MlE9aMM+2/sBbReyRGGEiTjkhuhU2CVrx9GNNWym4+DgtnXsxLBmMUFTNQub+izsnZVjnrwq8fcYgK9QlLhQlV/h[/tex]当[tex=2.286x1.286]qEpSh49SvBoNphcvks4d6w==[/tex]时,[tex=15.643x6.5]nLiEK20OJVLMd1LPkVEC8NpHEX1CHAroKXunN7eBnDiOTcmSyU04WbfH5MdxVWLL2bNDvtKtjUcRaNw2G8ixj0tZ/CfOiW4GplsjTNsuMYkK6vA5DDTJTfiUXDtCrmZTm6u3/6mx+euHbHCDHQtebmVu7AVLCup2LYCNv6PdbSXdMfJYVj4tSsvirJrCHRKAoArvRQeOYE+D7N8IF/5PyeR1rt1Lu8gsHASBII08+Ji4PzYypwOh+kAZhhXdNUT7[/tex]因此当[tex=2.286x1.286]qEpSh49SvBoNphcvks4d6w==[/tex]时,反常积分[tex=6.071x2.429]QDF3on418hztfquUcJypQYwtonQ+mFtQedEGxyAzTPBBJauFsgD+wTUcaYY8YVBM7TsP3lo1GIiuciBXniPdXw==[/tex]收敛;当[tex=2.286x1.286]JBgKJZ+lbuQZr7I+bjSCgQ==[/tex]时,反常积分[tex=6.071x2.429]QDF3on418hztfquUcJypQYwtonQ+mFtQedEGxyAzTPBBJauFsgD+wTUcaYY8YVBM7TsP3lo1GIiuciBXniPdXw==[/tex]发散。当[tex=2.286x1.286]qEpSh49SvBoNphcvks4d6w==[/tex]时,令[tex=16.643x2.429]jisq3IlcARyk0zdEUNMnuZx/16Ybd0uV/2COkaTIWuRpZrB3UXG0H6JPdt/Jhj46q43Evw4mnEdl0W7xKVL90g+TvJqHgVLsZ/2SvU9ChCgawjQg2r08s7XAgbOBkRju[/tex],则[tex=21.571x5.0]CWjFr6OsS6b0mIytFM6olOSKwbthdMARLjwbzAQasrsBxw9PxlO+7vpEc2kem8PnPdrp1V2jRIqy1FZvSPsw2Vk6vara0q3aIYe/CLTGYO33/kNKpP1H8l/TEEVTfJ72C8UWuZbjtH3dbnUSoNPcO2kM087k1z8F6wsz4RHmH6P5+cZCKUV3Ndju+Juc20kYygyjpbAs0k8fEC+YUSeHFEoOxd4G+Pc3CujsA6HapgstJFJJNkRC2vXhN/9NK8Vb[/tex]令[tex=3.929x1.286]xiHJGrow1qVACfsrazjytxY+Bi7xVMkVO/y+0B4mK+o=[/tex]得唯一驻点[tex=6.429x2.0]1j1GdDq8BfDdWhKNCVIiEjwhu/n4P0cWZJ63AKeaGek=[/tex]因为当[tex=7.857x2.0]ml2LxEK8Qa/BzP+cactejp9Tvv2U5jABB8LqWwo26w8=[/tex]时[tex=3.929x1.286]mLAKMX1Pqxl+JSZso+yRqKipku1oe9B8BPH8DEgszfs=[/tex],当[tex=6.143x2.0]PyjWx2UXI9ThrAD/sMCOCCRokNIj8OIm7Gg0nF/eMbI=[/tex]时[tex=3.929x1.286]h0EAajtyaQMRFTIUpUw9Rd3WkuxRlXGTNMPgZmWXbF8=[/tex],所以[tex=6.143x2.0]1j1GdDq8BfDdWhKNCVIiEsPOCuw26ALkoy5PbXrCoZg=[/tex]为极小值点,同时也是最小值点,即当[tex=6.143x2.0]1j1GdDq8BfDdWhKNCVIiEsPOCuw26ALkoy5PbXrCoZg=[/tex]时,这反常积分取得最小值。

    举一反三

    内容

    • 0

      当 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 为何值时, 广义积分 [tex=5.857x3.429]PJkWCDHq0HBl1uIZQZIQaCJeYEBINEa3r1jVRLOCV3RAYxRTzznIBmThvoc5BKDWEufXbmYTxx3twNmSd5TmhQ==[/tex] 收敛?又为何值时发散?

    • 1

      达峰时只与吸收速度常数[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex],和消除速度常数[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]有关。

    • 2

      证明定积分性质:[tex=11.5x2.5]ui4B5cEhfp2w4CiJQbWUaZmNFTvEtLyCHHNE309k/OYOc0S1nncp83+il/OGnmZUDr1K6x+PhPr23S5u+88CHA==[/tex]([tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]是常数);

    • 3

      利用归纳法,计算矩阵的[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]次幂,其中[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex] 为正整数:[tex=4.5x2.786]jyVOORWehIbTNQvvtYroWn+OoNUDMHtUiN0IB3CF6O90Qii1ad2ILxY0qDrd4G8UEJgLOPxdQvXt4vxZJSknZg==[/tex]。

    • 4

      利用归纳法,计算矩阵的[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]次幂,其中[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为正整数:[tex=8.286x2.786]jyVOORWehIbTNQvvtYroWodR1Ys8I+VOhRryrbtzHlxQvOL6QB6jtKHWE595Z7gWEr0L7OGEzJssPHWdW2v+X6QawGagb6DL2V2d2rVhd+hDmQDMzq3dCQTsVqNilb6VTygSl+WE8wcSJReXsGVNhQ==[/tex]。