Heine定理及其应用.pdf

目录

1引言·····································································································1

2文献综述·······························································································1

2.1国外研究现状··························································································1

2.2国内研究现状··························································································1

2.3国内外研究现状评价·················································································2

2.4提出的问题·····························································································2

3Heine定理及其不同结论···········································································2

3.1Heine定理的证明····················································································2

3.2Heine定理的推广····················································································4

4Heine定理的应用···················································································6

4.1判断、证明函数极限的存在性···································································6

4.2利用Heine定理求极限·············································································8

4.2.1求函数极限···························································································8

4.2.2求数列极限···························································································8

4.3证明函数极限的性质················································································9

4.4判断函数在某点的可导性·······································································11

4.5判断级数敛散性····················································································12

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4.6对函数fx的局部利用海涅定理，求函数fx的极限································