• 2022-05-31
    从点[tex=2.143x1.286]l9DYubvhJSmV7cTo/ad4fA==[/tex]引两条直线与曲线[tex=2.786x1.286]Xs9EyA29/UfxhGnFWoGIfw==[/tex]相切,求由此两条切线与曲线[tex=2.786x1.286]Xs9EyA29/UfxhGnFWoGIfw==[/tex]所围图形的面积[tex=0.714x1.286]yQZEV57S9rHjYvgfJydTyg==[/tex]。
  • 如图所示,设切点为[tex=2.929x1.286]AHSO9vFe0xmJ95kZuxl1+14YQCXx0Hgh1V1FKR8+M9LmjXiTajq0FqNoJ/ZnYN/N[/tex]则过切点的切线方程为[tex=9.286x1.286]X0xHkhQv17FwJmXiLxM8lYaRvdiyrdJx5/6mHK8ukkfAr/No0bWkqN8I8bC9PlqW[/tex],因为它通过点[tex=2.143x1.286]l9DYubvhJSmV7cTo/ad4fA==[/tex],即满足[tex=8.571x1.286]JnjadrDa9mEbI4Zteoz7m1oMj2RpZV79D0Y70gRP3GQ3XsktofwCjRJ+dO2uvFDc[/tex],即[tex=8.643x1.286]ppIwemms+fkUV2XHXjip0XYZzLez/5jj0IDCB928i9l/qj5dSIUAoynpiq1+lRK2[/tex],可得[tex=2.429x1.286]+EbSN7vzDCrSGfd8QSD+rQ==[/tex]或[tex=2.429x1.286]KTpHfis+vonhS/xr+XP9Wg==[/tex],即两切点坐标为[tex=2.143x1.286]q8d9ecMZwZI3gbdeOe+7AA==[/tex]与[tex=2.643x1.286]+J6I/nIMqbSbJ3BjHjv/FA==[/tex],相应的两条切线方程为[tex=2.571x1.286]oudOjkztyrnAY6Y1BpIJRQ==[/tex]与[tex=7.786x1.286]o04JFNo99lcIuVVxA7ljFGWCvrWbYVcDS9i7qQux9Jw=[/tex],选取[tex=0.571x1.286]Hz6y44ELFVLLNrLVhO3CQA==[/tex]为积分变量,则有[tex=11.0x2.786]V/9G9378YldSoVAKsVdSSHkOyRPpTzkUlvAuOXjclRxIjQwbmg9oukdb/6A29nVmGstT2D4MC+H5V5lcM5SeuzMnY+ZaeMmi7qbLa1T2SqY=[/tex][tex=12.214x3.0]l5YdkqXdnv+JuHJFx9uV8iHdlfVehCM3rBNlEAskotV+tEONG6xbszGZJczH3pZDGS3HySXqzbNRvODwHr1GxQHpIdCNe58uqBC0iiaLZGTkZn0eEXsw4DpBmoqdaPhitlPB+CjLbWGpbubJeqqQ7Q==[/tex][img=336x319]17838c202851c5d.png[/img]
    本题目来自[网课答案]本页地址:https://www.wkda.cn/ask/yojtexomoptjxto.html

    举一反三

    内容

    • 0

      求下列曲线所围平面图形面积:曲线[tex=5.143x1.429]/bMzoNPkMGqIXVfV4w5BWu2kDpNUFbOztYgfLZTUUDBZN0R2GdZrqWDhd47R27ih[/tex]与直线[tex=2.357x1.214]2BTdhDTzC18LiEPgyIZaCA==[/tex]

    • 1

      计算对弧长的曲线积分:[tex=3.571x2.214]9UG03GDhcYZHYVY4GZftYKGIbRvccYJfUYZ1HBvMGzc=[/tex],其中[tex=0.714x1.286]LA74ioWWkXdGbHCtFk/Sog==[/tex]为抛物线[tex=2.786x1.286]Xv1ex0v791LL5e/JRFQi6g==[/tex]介于点[tex=2.143x1.286]q8d9ecMZwZI3gbdeOe+7AA==[/tex]与点[tex=2.143x1.286]OGI1nc8WH38NKUnYUafisA==[/tex]之间的那一段弧 .

    • 2

      把对坐标的曲线积分[tex=10.643x2.214]9z1358KA5QP7tyaprc1EdF93uxXbeFhnRFApGbHH7PzEBem/KRzbr2mCxowOCkxS[/tex]化成对弧长的曲线积分,其中[tex=0.714x1.286]LA74ioWWkXdGbHCtFk/Sog==[/tex]为:沿抛物线[tex=2.786x1.286]Xv1ex0v791LL5e/JRFQi6g==[/tex]从点[tex=2.143x1.286]q8d9ecMZwZI3gbdeOe+7AA==[/tex]到[tex=2.143x1.286]OGI1nc8WH38NKUnYUafisA==[/tex]。

    • 3

      把对坐标的曲线积分[tex=5.071x2.214]S3T7aw2EkJGuQitaozRUnl4O7OCS098oQkUFuI40Lv4=[/tex][tex=3.0x1.286]/fFxW1CvOqgEw62SnVdMhw==[/tex]化为对弧长的曲线积分,其中[tex=0.714x1.286]LA74ioWWkXdGbHCtFk/Sog==[/tex]为抛物线[tex=2.786x1.286]Xv1ex0v791LL5e/JRFQi6g==[/tex]上从点[tex=2.143x1.286]q8d9ecMZwZI3gbdeOe+7AA==[/tex]到点[tex=2.143x1.286]v2wxUhEHgcEtjazZG/KOoQ==[/tex]的曲线弧 .

    • 4

      求下列曲线所围平面图形面积:曲线[tex=6.214x1.429]bBGbhGZ1lFtnqinZMvyS2OF7KqTC4r2JBHf6MO+9c2M=[/tex]与直线[tex=4.143x1.214]w0bFrtY530jJEOmoFzQ+/w==[/tex]