• 2022-07-27
    利用拉格朗日公式证明不等式:当[tex=5.929x2.214]zPLPjFYQ4mQ2fmWRMMNGOtCY4NB+x22M4zX5JVCAn9SD21BLupKLthzu9B5FP2nSGHHKAipj51HLeXfCnwTjlw==[/tex]时,[tex=6.429x1.357]O/i6qRt0yHnu8alpEjpHcKGLjsR+3tOn4MMcdwRnTKA=[/tex](等号只有在[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]时成立).
  • 不妨设[tex=9.643x2.214]syPBSBWS0N9yR8qxcbrQ9iVmJj2YosKdfC29NVBc+mCX+Sj3HTW+A/elbYNF3wpK/CdaCkyZp0s/ZsEawMp4ZQ==[/tex]在[tex=2.071x1.357]cn7zJO3/enLgpVEkACR0RQ==[/tex]上连续,在[tex=2.357x1.357]MXPQWNi+zHHCEzuZBSyPtw==[/tex]内可导,故拉格朗日定理成立,因而有[tex=21.643x2.786]byfeRxhLOo7GrUuSuXSLvlo5hZl1CUUvnboqYBB5NabUFvA+DpfR7IooBimms/PnHsitncu7tFdkbfhmq+J+RkdC/IsxoTAwMCg+O5+Qj4ehpMDJZj2YZEVMsnE3jCPM[/tex],则[tex=10.0x1.429]Fw9DjT8DSnx60NH14FY5rBROTJcYQDcPG+g5vu+0e5k1c/sGFDZ5oNAHaL5xTG/W[/tex]. 同理可证,当[tex=5.5x2.214]zPLPjFYQ4mQ2fmWRMMNGOmSagWrOtoc1VIpLhq+20qZ+4UvhUFKrFr++O745ruYw[/tex]时,[tex=5.857x1.071]YtZZiUiCREFS/iOR7ecMBA==[/tex].当[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]时,[tex=4.857x1.357]4/Yb9Cf0C1yCUHADTx+WHA==[/tex].总之,当[tex=5.929x2.214]zPLPjFYQ4mQ2fmWRMMNGOtCY4NB+x22M4zX5JVCAn9SD21BLupKLthzu9B5FP2nSGHHKAipj51HLeXfCnwTjlw==[/tex]时,[tex=5.429x1.357]yxofD8zRDiMDTpJlWnptrTiWHzWUPDPGvzzQ9ct5r/A=[/tex]成立.当[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]时,等号成立;当[tex=7.5x2.143]3/wc73mvAbtd8HiO9MdzuEMdm1RCgLmUZ7ofz5GCQ80=[/tex],[tex=6.0x1.429]wWUucM+n+MPR2570ymkAwcIeDaq07vDAiGCm2Zw9iMg=[/tex].故只能成立[tex=5.429x1.357]fenzEkurWeqoNeeH8lfRiA==[/tex].

    内容

    • 0

      >>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']

    • 1

      ‌下面说法错误的是( )。‌‌知识点:列表推导式‌ A: dict([(x, x**2) for x in range(6)]) 创建的字典是{0: 0, 1: 1, 2: 4, 3: 9, 4: 16, 5: 25} B: [[x*3+y for y in range(1,4)] for x in range(3)] 创建的是二维列表 [[1, 2, 3], [4, 5, 6], [7, 8, 9]] C: number = [-2, 4, 6, -5]string = 'ab'z = [(i, j) if i>0 else (-i, j) for i in number for j in string]这段代码创建的列表为[(2, 'a'), (2, 'b'), (4, 'a'), (4, 'b'), (6, 'a'), (6, 'b'), (5, 'a'), (5, 'b')] D: ' '.join([i for i in range(1,11)])的运算结果为字符串'1 2 3 4 5 6 7 8 9 10'

    • 2

      以下创建数组的方式错误的是() A: shortx[];x={1,2,3,4,5,6}; B: shortx[]=newshort[6];x[0]=9;x[1]=8;x[2]=7;x[3]=6;x[4]=5;x[5]=4; C: shortx[]=newshort[6];intlen=x.length;for(inti=0;i

    • 3

      【计算题】5 ×8= 6×4= 7×7= 9×5= 2×3= 9 ×2= 8×9= 7×8= 5×5= 4×3= 5+8= 6 ×6= 3×7= 4×8= 9×3= 1 ×2= 9×9= 6×8= 8×0= 4×7=

    • 4

      [tex=4.786x1.643]DU0rUnWXsXr0JAG1m3XeaAn37ASrg2xrNPV3iioolmI=[/tex] 在[tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex] 处的导数为______,在 [tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex] 处取得极______值.