全國高中數(shù)學(xué)聯(lián)賽分類匯編第03講導(dǎo)數(shù)

1、120092017全國高中數(shù)學(xué)聯(lián)賽分類匯編第03講：導(dǎo)數(shù)1、（2011一試4）如果，，那么的取值范圍是)cos(sin7sincos3355???????)20[????【答案】??????454??【解析】不等式)cos(sin7sincos3355???????等價(jià)于.????5353cos71cossin71sin???又因?yàn)?371)(xxxf??245()307fxxx????所以是上的增函數(shù)，所以，故()fx)(??????

2、cossin?Z)?????kkk(45242?????因?yàn)?，所以的取值范圍?20[??????????454??2、（2009二試2）求證不等式：，，2，…2111ln12nkknk????????????≤1n?⑵令，則，111ln11nnn??????????21ln1nnkkxnk?????112x?121ln111nnnxxnn?????????????211nnn???210(1)nn????因此1112nnxxx????

3、??又因?yàn)?11ln(lnln(1))(ln(1)ln(2))(ln2ln1)ln1ln1nknnnnnk???????????????????????從而12111ln11nnnkkkxkk???????????????12211ln111nkknkkn?????????????????????12111nkkkk????????????3所以，.32520rr???3152rr??4710rrrr??????去掉上面等式兩邊相同的項(xiàng)