高等数学讲稿.pdf

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1、
 !#"%$'&()*x)./0213#5+,-x!x0x!14limf(x)=0;6789f(x)&(:)*x)./021=<>?'@'*A+;-89BCDEF"HG'I'Jx!xx!1LK5>PQ0+M'N'Ojf(x)j4RR895STf(x)Jx!x0x!1LK<>?*5U<4limf(x)=1:8'9limf(x)=1"[

2、Z&AGIx!x0VXWXYf(x)x0+X,XX]X^X_'`2a=bcdNefgRhijk#5l'm&JK5l+M>0>0,no0M;R6789f(x)Jx!x0K<>?*ARf8X99"[ZJKAHGIlimx!1f(x)=1VXWXYf(x)jxjeX,XXpbcdNegRhijk#5l'm'&JK5l+M>0X>0,nojxj>Xbjf(x)j>M;R6789f(x)Jx!1K<

3、>?*Ar&(:)*)'./'021t5Wq2p.54+2s=R61(1)GIf(x)<>?5<>?@uf(x)R6(2)GIf(x)<>?@5vf(x)6=0,1<>?Af(x)8X9limf(x)=1"wZ&{hX

4、}Ax!x0+0VXWXYf(x)x0+X,XxX_X`yazbXcXdx0fg6GIlm&JK5lNe+M>0,>0,nox0?*A899

5、limf(x)=+1"ZJ@~KAzG'Ix!1VXWXYf(x)xeX,Xbc'dNefXgR6X7{hXiXjXkF5lm&X>0,JKX5l+M>0nXox<Xbf(x)>M;R89f(x)Jx!1K<>?*Ap2
limf(x)Alimx!x0f(x)limf(x)4x!1P>?@>'?@'AWq1.b-+89>?@>'?@'*'AWq2.b+''2"rrrrr9i>?@>?'@'*A1.+i2

6、.P>?@>?'@'*Ab-+6GIm&5vWq3.limf(x)=A,limg(x)=B,lim[f(x)g(x)]lim[f(x)g(x)]=AB=limf(x)limg(x):96i1.GIlimf(x)=Am&5c<5lim[cf(x)]=climf(x).96i2.GIlimf(x)=Am&5n<5nnplim[f(x)]=[limf(x)].6GIm&5vWq4.limf(x)=A,limg(x)=B,lim[f(x)
g(x)]lim[

7、f(x)
g(x)]=A
B=limf(x)
limg(x):6f(x)GIvm&5vWq5.limf(x)=A,limg(x)=B,B6=0,limg(x)f(x)Alimf(x)lim==:g(x)Blimg(x)96¡¢6P#£G'IWq6+2 limn!1xn=A,limn!1yn=B,(1)limn!1xnyn=AB;(2)limn!1xn
yn=A
B;6xn(3)GIyn6=0(n1),vB6=0,limn!1=A.ynB6GIWq7.(x)(x),lim

8、(x)=a,lim(x)=b,ab.2"rrrrr389j¤¥P"b¦+ZP(x)=axm+axm1+


+ax+a;01m1mQ(x)=bxn+bxn1+


+bx+b;01n1n6limP(x)=axm+axm1+


+ax+a=P(x);0010m10m0x!x06§limx!x0Q(x)=Q(x0);GIQ(x0)6=0,P(x)limx!x0P(x)P(x0)lim==:x!x0Q(x)limx!x0Q(x)Q(x0)89Jx!1K5P<¨DZa6=0;b

9、6=0#"b¦+008>>a0;Jn=mKu>>b0a0xm+a1xm1+


+am1x+ammKu(1)x!1b0x+b1x+


+bn1x+bn>>>>:1;Jn