高等数学教材 2.docx

高等数学教材2

第一篇：高等数学教材2目录一、函数与极限··························································································································21、集合的概念····················································································································22、常量与变量····················································································································32、函数·······························································································································33、函数的简单性态············································································································44、反函数····························································································································55、复合函数························································································································56、初等函数························································································································67、双曲函数及反双曲函数·································································································78、数列的极限····················································································································89、函数的极限····················································································································910、函数极限的运算规则·································································································11第二篇：高等数学21．“对任意给定的(0,1)，总存在正数N,当nN时，恒有xna2”是数列xn收敛于a的（）A充分条件；B必要条件；C充要条件；D非充分必要条件。imxnyn0。则下列断言正确的是２．设数列xn和yn满足ln（）。xn不存在，则limyn也不存在。B若xn无界，则yn必有界。A若limnnyn0。D若limC若xn有界，则limnn10，则limyn0。nxn一、填空题xna，则limxn１．若limnn２．对于数列xn，若x2k1a(k),x2ka(k)，则xn二、计算与证明题１．设xn的一般项xncosn，imxn?求出N，问l使nN时，xnnn与其极限之差的绝对值小于正数。当0.001时，求出数N。根据数列极限的定义证明：n2a22n121（１）lim；（２）limnn3n1n3第三篇：高等数学(同济大学教材第五版)复习提纲高等数学（同济大学教材第五版）复习提纲第一章函数与极限：正确理解、熟练掌握本章内容，求各类函数的