Bài tập toán cao cấp - Tập 2 pdf

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Bài tập Toán cao cấp tập 2 - Nguyễn Thuỷ Thanh

... c´o 2 x− x 2 x − 2 = 2 x− 2 2− (x 2 − 2 2)x − 2 =4· 2 x 2 − 1x− 2 −x 2 − 4x − 2 ·T`u.d´o suy r˘a`nglimx 2 2x− x 2 x − 2 = 4 limx 2 2x 2 − 1x − 2 − limx 2 x 2 − 4x − 2 = ... nˆen1+1 2 + ···+1 2 n= 2( 2n− 1) 2 n,1+13+ ···+13n=3(3n− 1) 2 · 3nv`a do d´o:lim an= lim 2( 2n− 1) 2 n· 2 · 3n3(3n− 1)= 2 lim 2 n− 1 2 n· 2 3lim3n3n− 1= 2 lim[1 ... ta c´o: 2+ 4+6+···+2n = 2+ 2n 2 · n;1+3+5+···+(2n +1)=1+(2n +2) 2 (n +1).Do d´oan=nn +1⇒ lim an=1.3) Nhu.ta biˆe´t:1 2 +2 2+ ···+ n 2 =n(n + 1)(2n +1)6 22 Chu.o.ng 7. Gi´o.iha.n...

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Bài tập toán cáo cấp tập 2

... c´o 2 x− x 2 x − 2 = 2 x− 2 2− (x 2 − 2 2)x − 2 =4· 2 x 2 − 1x− 2 −x 2 − 4x − 2 ·T`u.d´o suy r˘a`nglimx 2 2x− x 2 x − 2 = 4 limx 2 2x 2 − 1x − 2 − limx 2 x 2 − 4x − 2 = ... limx→1(1 − x)tgπx 2 (DS. 2 π)41. limx→11 − x 2 sin πx(DS. 2 π) 42. limx→πsin xπ 2 − x 2 (DS.1 2 )43. limx→0cos mx− cos nxx 2 (DS.1 2 (n 2 − m 2 ))44. limx→∞x 2 cos1x− cos3x(DS. ... ngu.o..cla.i (1 5 -2 6)15. limx→0√1+x + x 2 − 1x(DS.1 2 )16. limx 2 √3+x + x 2 −√9 − 2x + x 2 x 2 − 3x +2 (DS.1 2 )17. limx→05x3√1+x −3√1 − x(DS.15 2 )18. limx→03√1+3x...

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Bài tập toán cao cấp Tập 2

... c´o 2 x− x 2 x − 2 = 2 x− 2 2− (x 2 − 2 2)x − 2 =4· 2 x 2 − 1x− 2 −x 2 − 4x − 2 ·T`u.d´o suy r˘a`nglimx 2 2x− x 2 x − 2 = 4 limx 2 2x 2 − 1x − 2 − limx 2 x 2 − 4x − 2 = ... nˆen1+1 2 + ···+1 2 n= 2( 2n− 1) 2 n,1+13+ ···+13n=3(3n− 1) 2 · 3nv`a do d´o:lim an= lim 2( 2n− 1) 2 n· 2 · 3n3(3n− 1)= 2 lim 2 n− 1 2 n· 2 3lim3n3n− 1= 2 lim[1 ... ngu.o..cla.i (1 5 -2 6)15. limx→0√1+x + x 2 − 1x(DS.1 2 )16. limx 2 √3+x + x 2 −√9 − 2x + x 2 x 2 − 3x +2 (DS.1 2 )17. limx→05x3√1+x −3√1 − x(DS.15 2 )18. limx→03√1+3x...

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BÀI TẬP TOÁN CAO CẤP TẬP 2

... c´o 2 x− x 2 x − 2 = 2 x− 2 2− (x 2 − 2 2)x − 2 =4· 2 x 2 − 1x− 2 −x 2 − 4x − 2 ·T`u.d´o suy r˘a`nglimx 2 2x− x 2 x − 2 = 4 limx 2 2x 2 − 1x − 2 − limx 2 x 2 − 4x − 2 = ... 22 ; 0, 22 2; ,0, 22 2  n, Chı’dˆa˜n. Biˆe’udiˆe˜n andu.´o.ida.ngan=0, 22 2= 2 10+ 2 10 2 + ···+ 2 10n(DS. lim an =2/ 9)7 .2. Gi´o.iha.n h`am mˆo.tbiˆe´n 29 Tru.`o.ng ... hˆo.itu.1) an=n 2 − 1n 2 2) an =2+ 1 2! +13!+ ···+1n!Chı’dˆa˜n. T´ınh bi.ch˘a.ndu.o..csuyt`u.n!  2 n−1v`a do d´oan 2+ 1 2 +1 2 2+ ···+1 2 n−1=3−1 2 n−1< 3.4....