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1、èÆk)uia:china@gmail:com›Š1=²ŒÆ2006ê©Tomyparentsp11:1limn2004n+2005nn!1)‰.dpp2005n2004n+2005n2005n2p•limn2004n+2005n=2005.n!111:2lim(cosx)sin2xx!0)‰.1lncosx sinx 1=2lim(cosx)sin2x=Explim=Explim=e:x!0x!0sin2xx!02sinxcos2x1p+2p++np1:3limn!1np+1)‰.1p+2p++n
2、p1XnkpZ11plim=lim=xdx=:n!1np+1n!1nn0p+1k=1X1( 1)n2n+11:4¦?êxÚ¼êÚÂñ«•.2n+1n=0)‰.8<( 1)k1;n=2k+12k+1an=n=1;2;:0;n=2kèÆk)uia:china@gmail:com›Š2Kpnlimsupjanj=1n!1lÂñŒ»•1,q?êX1( 1)n2n+1n=0dLeibnizO{•Âñ,u´Âñ••[ 1;1].X1x2n+1n2ö,f(x)=( 1),Ù3[ 1;1]þ˜—Âñ,k2n+1n=0X1
3、Zxn2nf(x)=( 1)dn=00ZxX1n2n=( 1)d0n=0Zx1=d1+20=arctanx:2f(x)3(a;b)þëY,¿…limf(x);limf(x)•3.y²:f(x)3(a;b)þx!ax!b˜—ëY.y².Š8>>>>>:limx!bf(x);x=bKF(x)3[a;b]þëY,˜—ëY,•k3(a;b)þ˜—ëY,=f(x)3(a;b)þ˜—ëY.èÆk)uia:china@gmail:com›Š33ef(x)3x
4、0+•(x0 ;x0+)þk½Â,¿…3x0?†êÚmê•3.y²:f(x)3x0?ëY.y².df(x) f(x0)lim[f(x) f(0)]=lim(x x0)x!x+x!x+x x000=0f(x) f(x0)=lim(x x0)=lim[f(x) f(0)]:x!x x x0x!x 00•limf(x)=f(x0)=limf(x)x!x+x!x 00=f(x)3x0?ëY.4OŽ•‚È©Ix yx+yI=dx+dyLx2+y2x2+y2x2y2Ù¥L•÷ý+=1_ž••.a2b2x2y2)‰.">0¿©,¦x2+y
5、2"2•¹u+=1.dGreenúa2b2ª,•IIx yx+yx yx+yI=dx+dy=dx+dy=2:Lx2+y2x2+y2x2+y2="2x2+y2x2+y25f(x)3(0;1]þëY,¿…limf(x)=A;limf(x)=Bx!0+x!0+y²:82[A;B];9xn2(0;1);s:t:limf(xn)=:n!1èÆk)uia:china@gmail:com›Š4y².dK¿,supinff(x)=AB=infsupf(x)>00000)inff(x)sup
6、f(x)0 nnn·‚EêfxngXe:1)f(y)> 1½öf(z)<+1nnnnxn=yn½zn;2)f(y) 1…f(z)+1nnnndž,11f(yn) <+f(zn)nndëY¼ê0Š5,9xn2(yn;zn)½ö(zn;yn);s:t:f(xn)=u´fxngk5Ÿ:1)xn2(0;1)…limxn=0n!12)limf(xn)=.n!16f(x)´Rnþ¼ê,÷vlimf(x)
7、=+1,Ù¥x=(x;;x),1njxj!1n!1=2X2njxj=xk.y²:•3x02R¦f(x0)=inff(x).x2Rnk=1èÆk)uia:china@gmail:com›Š5y².dK¿,9A1>0;jxj>A1)jf(x)j>1f3k.48fxjjxjjA1jgþëY,k•Šm1.1)m11m1Ò´fƒ•Š2)m1>1•3n>m1,éTn,qdK¿,9An>A1>0s:t:jxj>An)f(x)>nÓ,f3fxjjxjjAnjgþk•Šmn(m1).·‚kmn´f•Š.nnþ,9
8、x02R;s:t:f(x0)=m=inff(x).x2Rn7f1(x)2R[a;b],-Zxfn+1(x)=fn(t)dt;n=1;2