函數(shù)與數(shù)列的極限的強(qiáng)化練習(xí)題答案含詳細(xì)分析

1、專(zhuān)業(yè)精神誠(chéng)信教育同方專(zhuān)轉(zhuǎn)本高等數(shù)學(xué)內(nèi)部教材嚴(yán)禁翻印1第一講：函數(shù)與數(shù)列的極限的強(qiáng)化練習(xí)題答案一、單項(xiàng)選擇題1下面函數(shù)與為同一函數(shù)的是（yx?）??2.Ayx?2.Byx?ln.xCye?.lnxDye?解：，且定義域lnlnxyexex????，∴選D??????2已知是的反函數(shù)，則的反函?f??2fx數(shù)是（）??1.2Ayx????.2Byx????1.22Cyx????.22Dyx??解:令反解出：??2yfx?x互換，位置得反函數(shù)

2、??12xy??xy，選A??12yx??3設(shè)在有定義，則下列函??fx??????數(shù)為奇函數(shù)的是（）????.Ayfxfx???????.Byxfxfx?????????32.Cyxfx?????.Dyfxfx???解：的定義域且??32yxfx??????????????????3232yxxfxxfxyx???????∴選C4下列函數(shù)在內(nèi)無(wú)界的是（??????）21.1Ayx??.arctanByx?.sincosCyxx??.s

3、inDyxx?解:排除法：A有界，B21122xxxx???有界，Carctan2x??sincos2xx??故選D5數(shù)列有界是存在的（）??nxlimnnx??A必要條件B充分條件C充分必要條件D無(wú)關(guān)條件解：收斂時(shí)，數(shù)列有界（即???nxnxnx），反之不成立，（如有界，M?????11n??但不收斂，選A6當(dāng)時(shí)，與為等價(jià)無(wú)窮n??21sinn1kn小，則=（）kAB1C2D212解：，選?2211sinlimlim111nnkknn

4、nn??????2k?C二、填空題（每小題4分，共24分）專(zhuān)業(yè)精神誠(chéng)信教育同方專(zhuān)轉(zhuǎn)本高等數(shù)學(xué)內(nèi)部教材嚴(yán)禁翻印3????221f???????故????221fxx??15設(shè)，的反函數(shù)??fxlnx???gx，求????1211xgxx????????fgx解:（1）求∴反22():1xgxyx????解出：x22xyyx???22xyy???互換位置得xy()22gxxx???(2)????lnln22fgxgxxx????????16

5、判別的奇偶性。??fx??2ln1xx???解法（1）：的定義域，關(guān)??fx??????于原點(diǎn)對(duì)稱(chēng)????2ln1xxxf??????2ln11xx?????122ln1ln()1xxxx??????????fx??為奇函數(shù)??2ln(1)fxxx????解法（2）：????fxfx?????22ln(1)ln1xxxx?????????22ln(1)1ln10xxxx?????????????故為奇函數(shù)????fxfx??????fx

6、17已知為偶函數(shù)，為奇函數(shù)，??fx??gx且，求及????11fxgxx?????fx??gx解：已知()()fxgx???11x????即有1()()1fxgxx???????1()()1fxgxx??????2?得????2?????11211fxxx????故21()1fxx??得????2????11211gxxx????故2()1xgxx??18設(shè)，求的值。32lim8nnnana???????????a解：3323liml