详细讲稿：第二章 导数与微分(考研).doc

2009 考研数学强化班讲稿高等数学张天德版权所有翻录必究 2017-02-23 1 第二章导数与微分题型一利用导数定义 0 0 0 1. (0) 0 ( ) (0) ( ) '(0) lim lim 0 lim( 1)( 2) ( ) ! x x xf f x f f x f x x x x x n n ? ????? ??? ?????解?? 2 '( ) "( ) '( )( ) 2( ) ( ) '( ) "( ) '( ) '( ) '( ) lim lim '( )( ) 2 ( ) 2 ( ) x a x a x f a f x x a x a f x a f a x a a x a f x x a f x f a ??? ????? ????????? ??? 220 202 2 2 2 2 0 0 '0 ( ) 3. ( ) 0 lim 1 lim ( ) 0 (0) , 0 0 ( ) ( ) (0) 1 lim lim ( ) (0) lim (0) ( ) h h h h x f h f x x h f h f h x h x f h f h f h h f x f fxC ??? ????? ?? ??? ????? ?? ??+ +解由在点连续且知令则当时, == . 2解极限为e 2009 考研数学强化班讲稿高等数学张天德版权所有翻录必究 2017-02-23 2 000 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 ( ) ( ) lim ( ) ( ) ( ) ( ) lim ( ) ( ) ( ) lim ( ) '( ). x x x x x x xf x x f x x x xf x x f x x f x x f x x x f x f x f x x x x f x x f x ?????? ?????? ??? ? 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 0 0 ( ) , lim[ ( ) ( 3 )] 2 ( ) ( ) ( 3 ) ( ) 0 lim ( ) 0 (