利用极限存在准则证明下列数列极限存在，并求出极限值：[tex=5.857x1.429]muVZAvTxmlL3rAhE6jQXHxffyPtpZm35MnQyO7Rfvyc=[/tex]，[tex=3.143x1.5]a4D1L0Am8jTDa+u9dlc13Q==[/tex].
举一反三
- 利用极限存在准则证明:数列[tex=19.0x2.786]UebQy5BR388uInyUKzqkBTcpxc/5aZkJ1Yhi7JFHjcbGGT5W2KENUZnijrLXRP/I6nVuygERkOAjyN0DcZdIcD8xqAxKAxcorujQwrnk6bGYuZNScYdzUxO0MbP2VOc5[/tex]的极限存在并求[tex=3.0x1.714]OqU0SQaVHd2x+OGLCy0gvcSD1JSooLY5K80iiCjWVQetN8mKChAvoCV6ZQx1TdT3[/tex]
- 利用单调有界数列收敛准则证明下列数列的极限存在.[tex=10.143x2.429]PQFiji/X+PAXK5Mf5O9sysjL7nxlk8iGb2TkUn4RS04/yFW9ARVojzc5JrGVjglG[/tex].
- 观察下列数列的极限是否存在,如果存在,求出极限(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)
- 证明下列数列极限存在，并求其值：[tex=6.357x2.0]HjmnHEf023+GWSYusdiEXrNZsNEAwRK2g2Rbmq2fI8Ky2PavH8zyGzoiJkvIbLAp[/tex]，[tex=4.714x1.214]x47x5P3f6WLekSINWqUdEw==[/tex]
- 先求出半无界区域上波动方程的定解问题[tex=16.286x5.5]fnpmC2J6JmQBLyo5NmGAzz1EEFvh0W+KMVB3PRTO6PCE68CPHabueHXn53RXfqgSv6yqnPmHws7mdx/v1wD39H8TNSf4IS7/FerIbYVvvrjqRE86XgwXknsfdFBaIMo3BTKCZFTfeuS9s0zFtrDiOryNUqUhkPR5UsfiBNy72F5LOc44IDeCjAaZa4kGfp5jGGdk7GyJ3xjFTSqjBqP0Lg==[/tex]的解u(x,t)，然后证明对任意c>0，极限[tex=5.929x1.857]MhC0sa4kP8ihnFHLNuEHS25qEA5Cb518i4FFAO8pXj9KLX20w+hXVQBY8P+o6ph/[/tex]存在，并且求出该极限.