• 2022-06-08
    试将函数[tex=6.429x2.786]KxH31rE037r1nCSwh+zvwDWZtD0vGCZcTP5ojFn1RXTeEMgTG7/cDYJn2GGp5OK5[/tex]展为麦克劳林级数,并写出其收敛域.
  • 解 因为[p=align:center][tex=17.286x2.786]6DVy4pGkr/W+qEjHWalRbRIa/VMJhwlNGNAKljZEmhcni/JUAVkzRWBtTfYnhJEJdveGooSlZb3VltduTnCtf2DrF/YdXPMACSpg2hnjwjkDXd9InGAzbHo/ayhIv8gq[/tex]下面分别将 [tex=12.143x2.643]Ojv4efBlg/Z+vZLqz2BlbLjOTD2i66/qFdkNyBLFbRuQgH6WuDlm80ZnzC1XoKm4Ln6Gi4TKIPkMZikoxLqN3A==[/tex]展为幂级数, 因为[p=align:center][tex=21.0x6.5]qeiYnKXLEhyhuGRg8yLtr1pZryuFg87W6+e1kRecyMammu5WnvssWoDPOr/kCHAIU41K1B53GCRNiF9yI7JvC/fzVw4taHWJVyQ2HIHgeD2QXtK4bxityMWa40zLpRubQtDE1Dw0u1LRKryLHXhua/ZV1eyiY9Na/VogRStvUm+aOSrH2YqHElml6DCcr/KXY13R87rH2cpdBk0Xcx2XNCZz2XEaPf3/ZfVghDBrdHCitC4tNrBQZPFQi3ol+Xs2pYh3daxyv/a/uv4YDYGiypqkdVm7Vg+P1AcKpDh5Cu9d/QUp060Ac52dkrbh1iAeVPl7sO/mzuxk6K5ZOuuKyQFajpOzgdlkVCobhn2YzX4=[/tex]两边求导得[p=align:center][tex=19.0x3.286]IndZ1lplfkYQKlk7dMrnc8z7BRJLNiI0SN4zqHsgUGNptKxtNGpVryYd3BgMYXVA4p0/kbMEJiEvJokH2Uc5KiaoRxysScwMPd5kFSPedDXb8udACBiJV8h5f39b2FnjBZMYK5HZqOno0Th8BAJn64uW51hBNjn3MPlg3p9jRVBF7UrhotaDNEKfex844+PH[/tex]又因为[p=align:center][tex=24.143x3.286]QCKlkVP7wzChrnNHGjpxsuZh71jKhfQW3n5KASwY55tgd86QsE/M8r8WahN2BJL8NTaxXmlzMLIyrqeRtnMuAH6x2AaViImwsK9H91zoEFUFZByZJU77M6vgunJc4N2808PTayJ89JqJXG9pA8gZLdvT+bK4/CaZZzayY7tDD1NTSg8Os2ZVc2+OS7EkcGu5OiGq+anlHy70EB5qTltdNQ==[/tex][br][/br]所以 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]的幂级数展式为[tex=21.643x6.929]qeiYnKXLEhyhuGRg8yLtr3TRXPbp1xU2kWEXXpQr5FZePTzvHh4MgdUDyshuifiDiFkd+cb/1FgrlgFWI9otWpFLQMIqq1+VYgrUpqc4IfKaJkYgAqiuQbXQz/AMxm4Omicu74LTyjINorxXGXy7NtPQRhnrYu9RU7S6SOyPCcy3qFz2n0kP5bykptNye39txjTfH4xW+MoxcGALvI7Qfx9Bxdg+PjFDHSkgYXHkxX+aq+78asdXDppBJR5azyGMLde9sG2GcjwjETavNAM/E3vDcnICZMHgXIUnI6C0l1MaR9FfiwLKafE6XpyrWtY1L59ZTP/kAGR+iVEhVgNlUQ==[/tex]其收敛域为[tex=3.0x1.357]NCAdZ4qexY1dalX8ydh4Jw==[/tex] 与 [tex=3.214x2.357]rlH3MEOCcTJnqM5sKtPm2fl/Y9jAnxc4KxJ3c5H2p3Q=[/tex]的交集,即 [tex=3.214x2.357]rlH3MEOCcTJnqM5sKtPm2fl/Y9jAnxc4KxJ3c5H2p3Q=[/tex].

    内容

    • 0

      将此函数展开成麦克劳林级数,并求其收敛域:[tex=7.786x2.357]t/eIiKQYSkv9FsOKizKhSWmREf8EXhvvBww1L0h5cvHgfAnnho/AMhp1CUHAtEi1[/tex]

    • 1

      用间接法将下列函数展开为麦克劳林级数,并指出其收敛域: [tex=4.071x1.0]i3Dyl7rzFZgnl96sbxZqOQ==[/tex]

    • 2

      用间接法将下列函数展开为麦克劳林级数,并指出其收敛域: [tex=4.857x2.429]SNda6Kz+EFN2fXzDb2IvIJGlvnAojuTx4c58CVfCEq0=[/tex]

    • 3

      用间接法将下列函数展开为麦克劳林级数,并指出其收敛域:[tex=6.071x1.571]He/EmZodQU4JQnyIE90ZzI8hoXYC3jhy4pAbDxNWtIA=[/tex]

    • 4

      用间接法将下列函数展开为麦克劳林级数,并指出其收敛域:[tex=3.643x2.714]vVtLLbNY4gvkEZHWdUVBVWuysChRPHE54sZ/lxZf8HauXO+jTOYktBnTZVhFxouE[/tex][br][/br]