利用数列极限的定义证明极限:[tex=4.714x2.357]OqU0SQaVHd2x+OGLCy0gvYudstXsA8dnxqkmKhl/YeXm39Hh87dzFhpQT2fRrjQHYrO/TC9zvSO/xTpCzXMfJA==[/tex]

2022-06-01

利用数列极限的定义证明极限:[tex=4.714x2.357]OqU0SQaVHd2x+OGLCy0gvYudstXsA8dnxqkmKhl/YeXm39Hh87dzFhpQT2fRrjQHYrO/TC9zvSO/xTpCzXMfJA==[/tex]

答案：

证明:对[tex=2.857x1.071]wnnVw3AI26tAAle5k2adK4NGRjcq1HkxnLwWLrrrs4o=[/tex],若使[tex=5.143x2.786]a1fmphWeATIoLwLUVgnTYBZXfxbV0Wc5fzhQ0QaP8YHudlKPI+KM+aU58T03k7xn[/tex], 即[tex=3.786x2.857]KH4ydOuG5owQ73+5VKajZzij8RsYbIVQn9ayQpY0zfqklyLtiPERrdpSo007/VtA[/tex], 取[tex=4.714x3.357]KFZ16mdpoac8paAfJu+ISZB/hXMOnzKXG6DtmVDyGngIQC72126wci30QrdM2hj0[/tex] .对[tex=2.857x1.071]wnnVw3AI26tAAle5k2adK4NGRjcq1HkxnLwWLrrrs4o=[/tex],当[tex=2.786x1.071]yThi63usA2LCCH2wVROBcg==[/tex]时,有[tex=5.143x2.786]a1fmphWeATIoLwLUVgnTYBZXfxbV0Wc5fzhQ0QaP8YHudlKPI+KM+aU58T03k7xn[/tex],故[tex=4.714x2.357]OqU0SQaVHd2x+OGLCy0gvYudstXsA8dnxqkmKhl/YeXm39Hh87dzFhpQT2fRrjQHYrO/TC9zvSO/xTpCzXMfJA==[/tex] .

举一反三

内容

0
利用数列极限的定义证明极限：[tex=6.643x2.786]OqU0SQaVHd2x+OGLCy0gvbnBdqyRL3fXll51asuCZWnhRqsKxAfB+RVzpHXh/K3s7nwHnn1UPBmlejRVcdpWlg==[/tex]
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
用数列极限的定义证明极限:[tex=7.857x2.786]OqU0SQaVHd2x+OGLCy0gvbnBdqyRL3fXll51asuCZWmX29RczN3vjQ/eZ99qnEkg9ppbxvi6kfViL6BqtNsH5w==[/tex]
3
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.
4
根据数列极限的定义证明极限：[tex=6.143x2.0]I5PocycXYSmqX9keDWPEO3D+UX8eE8/zgBb1EQOUoWe3xYl0xg1p6qimZaq6Vt8EH8WQLMW0Jz6E/xZvJ+QUGQ==[/tex] .