1、 F l T p K *李 null 萍 null 成立花 null (西安工程大学理学院 null 西安 null 710048)K null 1 null l T + 0 , p B K H , T ? F l T ,5 V h l 9 1 o M null l T ; T ; K null null S s | null O 172 s Q B , Q f M 1 M M y . B f 5 T # E 5 9 , 1 1 l 9 F Z L , , l T 5 T $ j .7 , H W K = 9 E l T p K B 5 Z 7 .o null8 “ 5 B ! $ l B 1
2、 , B 5 , T Q l , Y , l . l T , 5 l T p K F , l B j .B a l T! f y = f (x ) x0) V , 5 / T 0 :1null f #(x 0 ) = limxx0f (x ) - f(x0 )x - x02null f #(x 0 ) = limh 0 f(x0 + h) - f(x0 )h h k l , V nullx( nullx = x - x0 )anullx f V r T .= a F l T p K 1null limx 0 x2 + p 2 - px2 + q2 - qnull (p 0, q 0)s nul
3、l N 5 x 0 H 00 T , Q - , Z E h s , y 0 , 5 + , s as 0 H L V p . l T , 9 V l T p . null 7 f(x) = x2 + p2, g(x) = x2 + q2 T = limx 0 x2 + p2 - px2 + q2 - q= limx 0f(x ) - f ( 0)x - 0g(x ) - g( 0)x - 0= f #( 0)g#( 0) = pq 2null p K limx 0 (ex + e2x + % + enxn )1x , n 1 .18 STUD IES IN COLLEG E M ATHEM
4、AT ICS null null null null null null null null null nullV o lnull10, N onull5Sep. , 2007* l : 2007 - 01 - 05s null N K T x 0 H 1f( n+ 1 ) (x) 0(x ( (a, b) ) H , nullx ( (a, b f(x ) )nk= 01k! f( k) (a) (x - a) k;f( n) (x ) 0(x ( (a, b) ) H , nullx ( (a, b f (x ) )n- 1k= 01k! f( k ) (a) (x - a)k;f( n+
5、 1 ) (x) 0(x ( (a, b) ) H , nullx ( (a, b f(x ) )nk= 01k! f( k) (a) (x - a) k.- + 0 % , T X ,9 T ay lor T f . 3 : T 5 ,7 Tay lor T % 5 . I D 1nullv I . V 3 I k 5 M . g : g v , 2004. 2 I k . S V 3 d B I k I k s M . : , 2006.null(上接第 19页 ) 6null ! f f(x) x = 1) V , p Klimx 0 f ( 1 + x) + f (1 + 2sin x
6、) - 2f ( 1 - 3tan x)xs null 5 T A 1 , - % 4 ? C x 0 H 00 T , 5 ! ? V l T ? p N K . null T = limx 0 f ( 1 + x) - f (1)x + f (1 + 2sin x) - f (1)2sin x 2 sin xx - 2 f ( 1 - 3tan x)- 3 tan x - 3tan xx = f #(1) + 2f #(1) + 6f #(1) = 9f #( 1) 7null ! a + 0 , f (x ) V , p K limt 0 1t f(x + ta ) - f(x - ta
7、 ) . null K T a M ,5 V l T p .limt 0 1t f (x + ta ) - f (x - ta ) null null null null null null null null= limt 0 f (x + ta ) - f(x)ta+f (x - ta ) - f (x)- ta 1a = 2af #(x ) + 5 V ? C , p x x0 H 00 T K H , T ? % 4 MY , F l T , 5 V | 5 e . I D 1 6 v i . ( ). , 1996 2 Pnull 6 Jnull : . u X 5 “ . S , 200324 null null null null null null null null null null null null null null null null null 2007 M 9