利用数列极限的定义证明极限：[tex=6.643x2.786]OqU0SQaVHd2x+OGLCy0gvbnBdqyRL3fXll51asuCZWnhRqsKxAfB+RVzpHXh/K3s7nwHnn1UPBmlejRVcdpWlg==[/tex]
证 对任意给定的[tex=2.357x1.071]zaTYmiB02c3fW3zvAQdizg==[/tex](不妨设[tex=4.857x1.357]uX1WpgBfcuVUmsE0jLtNfz2DTOABJ9l8Xi/sdBg2Ue0=[/tex]要使[tex=8.429x2.786]R/OPV7I5oNPOLDfiwuMYs3vBKpXgoZqYRq8p0P8maBez84lSsiRajm0ZVsdVFH9Wmp1N/Qy/y4TWYz/zDZyFgOqUEBAXp+Tr2MjdWNbjBzU=[/tex]只需[tex=18.071x2.786]N7aBuIoPqJrXifsisdPa2SieS2NbQ2hy+otcYven+NK6zQQAmL98QS6/pN7HGCeRtSb3zEEzom/GT7Dr5mx7ZlfbTVbS74TVCXUkdWBa03Pw73KeKXO/3AfEHeA8LR+kJZpQwU7R4bCIXEGpQGIcBwSsGIawNTnnJDBr2GgEEsne9/YjK6FydEmZKw/h659R[/tex]取正整数[tex=11.214x2.786]SnEEL+rJADO55RcwEZo1AC3VXYW5pIAP793StDc8CKH3gRlyrXsI34T2mEXyLy8Vs628TNQx45hTf26qUyDeuzE5RWI61LqPLMRFqZJIvuIbyPZklXM0F//IF67sZkTu[/tex]则当[tex=2.786x1.071]yThi63usA2LCCH2wVROBcg==[/tex]时,恒有[tex=7.143x2.786]tsjHSH6j2jeAmBMmjwWx0oQhgrUM6HdBldYsHS4c1t15n5G89+4o3D8pUlQ0KUzHXXWN5W58SH43jAUu09pl8tJdFUcT5XcU2MsbDloMsio=[/tex]因此[tex=7.071x2.786]Q9IYTFR3kTY3iJCCC2wa72hfjSzrNpaMNw1974QpoR+R+xDvDNbFXYjCJjrJpqHUBM3u9CnzINw8YZ9ARYqx+V/quUVXEgA4OYX5c65wBro=[/tex]
举一反三
- 利用数列极限的定义证明极限:[tex=7.714x2.786]OqU0SQaVHd2x+OGLCy0gvbnBdqyRL3fXll51asuCZWkzJRNbRTxtQBWcnJIRZuQfTMdKgbJsbsgTzq9i0FvwfQ==[/tex]
- 利用数列极限的定义证明极限:[tex=5.714x2.357]OqU0SQaVHd2x+OGLCy0gvYudstXsA8dnxqkmKhl/YeVci09YKfX4g3o11IxHTNktOH5pRM1HlOt4cFOqsW5YWQ==[/tex]
- 利用数列极限的定义证明极限：[tex=6.429x2.571]OqU0SQaVHd2x+OGLCy0gvYudstXsA8dnxqkmKhl/YeUsEV4bOkkz4aN0dhGrKa5YZMtS6BjUPl5RW3tIeLIkZw==[/tex]
- 利用数列极限的定义证明极限:[tex=4.714x2.357]OqU0SQaVHd2x+OGLCy0gvYudstXsA8dnxqkmKhl/YeXm39Hh87dzFhpQT2fRrjQHYrO/TC9zvSO/xTpCzXMfJA==[/tex]
- 利用数列极限的定义证明极限：[tex=7.714x2.643]OqU0SQaVHd2x+OGLCy0gvYudstXsA8dnxqkmKhl/YeWnbaukoJ1kkLu3vA7ffucz2ZhoeYX30iiCUNdEznVxtw==[/tex](a为常数)
内容
- 0
【单选题】极限 lim x → 0 1 − cos 3 x x sin 3 x 的值为? A. 0 B. 1/6 C. 2/3 D. 3/2
- 1
利用数列极限的定义证明下列极限：[tex=6.929x2.643]8vJYfWnQRBqJWdmg/yoyrF/P4fDe8/QlFA2tXTksR5Y/bDNMfglfCRTHcizBWXcDqfuC58QfoUzfZw7+Cy6cjQ==[/tex]
- 2
试用定义1证明：(1) 数列[tex=2.357x2.786]YfOpfsXU462gw1PTp8mUhnyox9SPD+a41vcy562G3qQ=[/tex]不以 1 为极限[br][/br](2) 数列[tex=3.643x2.786]hn0grm0nFoK1+B+qN90oORmIO38IPAPRNvMSoSSLroY=[/tex]发散.
- 3
求下列极限：(1)lim(x→0)(∫x0ln(1＋2t^2)dt／x^3
- 4
用数列极限的定义证明极限 :[tex=5.857x2.214]OqU0SQaVHd2x+OGLCy0gvYudstXsA8dnxqkmKhl/YeW4R2Q7Xs2LKvHAti+OG9bS[/tex]