数学竞赛讲座.ppt

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1、数学竞赛讲座,一、函数极限与连续,1.设,证明：,证明：,利用夹逼准则，取极限可以证明,2.证明：,证明：考虑,利用夹逼准则，取极限可以证明,3.证明：,证明：,利用夹逼准则，取极限可以证明,4.证明：,证明：,利用夹逼准则，取极限可以证明,5.设,证明：,归纳法可以证明,证明：,6.设,证明：,证明：,7.设,证明：,证明：,8.设,证明：,证明：,9.设,证明：,10.设,证明：,11.设,求：,解：,12.设,求：,解：,或,13.,求：,解：,14.设,求：,解：,15.,求：,解：,16.,求：,解：,17.,求：,解：,18.,求：,解：,或,19.,求：,解：,20.设,求：,解

2、：,21.,求：,解：,22.,求：,解：,23.,求：,解：,24.设,求：,解：,25.,求：,解：,26.,求：,解：,27.,求：,解：,28.,求：,解：,29.,求：,解：,30.,求：,解：,31.,求：,解：,32.设,证明：,证明：,33.设,解：,34.讨论,解：,35.讨论,解：,36.,解：,37.,解：,38.,解：,39.,解：反证法：假设存在,40.,解：,41.,解：,42.,解：,43.,解：,44.,解：,45.,证明：,46.,证明：,47.,证明：用定义,48.,证明：,用定义,49.,证明：,50.,解：,51.,解：,52.,解：,53.,解：,54

3、.,解：,55.,解：,56.,解：,57.,解：,58.,解：,59.,解：,60.,解：,61.,证明：,62.,证明：,63.,证明：,64.,证明：,65.,证明：,66.,证明：,67.,证明：,68.,证明：,69.,证明：,70.,证明：,71.,证明：,72.,证明：,73.,证明：,74.,证明：,75.,求：,解：,76.,证明：,77.,证明：,78.,证明：,79.,证明：,80.,证明：,81.,证明：,82.,解：,83.,解：,84.,证明：,85.,解：,86.,证明：,87.,证明：,88.,证明：,89.,证明：,90.,证明：,91.,证明：,92.,证明：,93.,证明：,94.,证明：,95.,证明：,96.,证明：,97.,证明：,98.,证明：,99.,证明：,100.,求：,解：,101.,证明：,102.,证明：,103.,证明：,在条件,求,下条件极值,令,所以,是全局最大值,104.,解：,