Tich-phan-Ly-thuyet-va-bai-tap

Tich-phan-Ly-thuyet-va-bai-tap - Tran S Tung Tch phan Nhac...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Traàn Só Tuøng Tích phaân Trang 1 Nhaéc laïi Giôùi haïn – Ñaïo haøm – Vi phaân 1. Caùc giôùi haïn ñaëc bieät: a) = x0 sinx li m1 x Heä quaû: = x li = u(x )0 sin u(x) li u(x) = u(x) li sin u(x) b) x x 1 lim 1 e , xR x fi¥ +=˛ ²³ Ll Heä quaû: 1 x lim ( 1 x ) e. += ln( 1 x) li x + = x e1 li x - = 2. Baûng ñaïo haøm caùc haøm soá sô caáp cô baûn vaø caùc heä quaû: (c)’ = 0 (c laø haèng soá) 1 ( x ) 'x a a- =a 1 (u ) ' u u' a 2 11 ' xx =- 2 1 ' uu ( ) 1 x' 2x = ( ) 2u = (e ) 'e = ' u'.e = (a ) ' a .lna = ' a .lna. u' = 1 (lnx)' x = (ln u)' u = a 1 (lo g x ') x.lna = a (lo g u)' u.lna = (sinx)’ = cosx (sinu)’ = u’.cosu 2 2 1 (tgx) ' 1 tgx co sx = =+ 2 2 (tgu) ' ( 1 tg u).u' co su = 2 2 1 (cot gx) ' ( 1 cotg x) si nx - = = -+ 2 2 (cot gu) ' ( 1 cotg u).u' si nu - = = 3. Vi phaân: Cho haøm soá y = f(x) xaùc ñònh treân khoaûng (a ; b) vaø coù ñaïo haøm taïi x (a; b) ˛ . Cho soá gia D x taïi x sao cho x x (a ; b) +D˛ . Ta goïi tích y’. D x (hoaëc f’(x). D x) laø vi phaân cuûa haøm soá y = f(x) taïi x, kyù hieäu laø dy (hoaëc df(x)). dy = y’. D x (hoaëc df(x) = f’(x). D x AÙp duïng ñònh nghóa treân vaøo haøm soá y = x, thì dx = (x)’ D x = 1. D x = D x Vì vaäy ta coù: dy = y’dx (hoaëc df(x) = f’(x)dx)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Tích phaân Traàn Só Tuøng Trang 2 NGUYEÂN HAØM VAØ TÍCH PHAÂN 1. Ñònh nghóa: Haøm soá F(x) ñöôïc goïi laø nguyeân haøm cuûa haøm soá f(x) treân khoaûng (a ; b) neáu moïi x thuoäc (a ; b), ta coù: F’(x) = f(x). Neáu thay cho khoaûng (a ; b) laø ñoaïn [a ; b] thì phaûi coù theâm: F'(a ) f(x ) va ø F'(b ) f(b) +- == 2. Ñònh lyù: Neáu F(x) laø moät nguyeân haøm cuûa haøm soá f(x) treân khoaûng (a ; b) thì : a/ Vôùi moïi haèng soá C, F(x) + C cuõng laø moät nguyeân haøm cuûa haøm soá f(x) treân khoaûng ñoù. b/ Ngöôïc laïi, moïi nguyeân haøm cuûa haøm soá f(x) treân khoaûng (a ; b) ñeàu coù theå vieát döôùi daïng: F(x) + C vôùi C laø moät haèng soá. Ngöôøi ta kyù hieäu hoï taát caû caùc nguyeân haøm cuûa haøm soá f(x) laø f(x)dx. & Do ñoù vieát: f(x)d x F(x )C =+ & Boå ñeà : Neáu F ¢ (x) = 0 treân khoaûng (a ; b) thì F(x) khoâng ñoåi treân khoaûng ñoù. 3. Caùc tính chaát cuûa nguyeân haøm: ( ) f(x)dx ' f(x) = & af(x)d x a f(x)dx ( a 0) =„ && [ ] ) g(x ) d x x g(x)dx +=+ & [ ] [ ] f(t)d t F(t ) C f u(x ) u'(x)d x F u(x F(u ) C ( u u(x)) = + ± = + =+= 4. Söï toàn taïi nguyeân haøm: Ñònh lyù : Moïi haøm soá f(x) lieân tuïc treân ñoaïn [a ; b] ñeàu coù nguyeân haøm treân ñoaïn ñoù. §Baøi 1 : NGUYEÂN HAØM
Background image of page 2
Traàn Só Tuøng Tích phaân Trang 3 BAÛNG CAÙC NGUYEÂN HAØM Nguyeân haøm cuûa caùc haøm soá sô caáp thöôøng gaëp Nguyeân haøm cuûa caùc haøm soá hôïp (döôùi ñaây u = u(x)) d xxC =+ & d u uC & 1 x x d x C ( 1) 1 a+ a a„- & 1 u u d u C ( 1 a & dx ln x C ( x 0) x = +„ & du ln u C ( u u(x ) u = + =„ & xx e d xeC & uu ueC & x x a a d x C ( 0a lna = + <„ & u u a u C ( = + & cosxd x sin xC & cosud u sin uC & sin xd x cos = -+ & sin ud u cos = & 2 2 ( 1 tg x)d x tg co sx = + && 2 2 ( 1 tg u)d u tg co su = + 2 2 ( 1 cotg x)d x cot g si nx = + = 2 2 ( 1 cotg u)d u cot g si nu = + = x C ( x 2x = +> & u C ( u 2u = & 1 cos(a x b)d x sin(a x b ) C ( a a + = + & 1 sin(a x b)d x cos(a x b ) C ( a a + = - + & d x1 ln a xbC a xba = ++ + & a x b a xb 1 e d x e C ( a a = & d x2 a C (
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 152

Tich-phan-Ly-thuyet-va-bai-tap - Tran S Tung Tch phan Nhac...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online