2) = = = =0
t= , t→0 x→0, y→0
. f(1,2,,n) , , , , , .. +¥.
, .
. f() ̮0,
=0.
f() ̮0,
=¥, +¥, -¥.
, , . , , .
.
1. f() ̮0 , f()-0 ̮0.
f() ̮0 , f()=+a(1,2,,n), a(1,2,,n) .. ̮0.
2. , ,
=×
3. , ,
=
.
4. , ,
= ×
.
5. , ¹0, ,
=
6. 0 ()£f(M)£g(M) = =, =.
.
f(1,2,,n) , , . n- (, .. n=2,3,..), .
f(,).
, , ( ) , , , ( ) b. ´.
, , ()= . (a,c] . , (a,c], ..
=j(), Î(a,c].
m= . m f(,) (,b):
m=
y (b,d] . y, (b,d], ..
|
|
=y(y), yÎ(b,d].
n= . n f(,) (,b):
n=
. f(x,y)= (0,0) , (0,0) .
1) ¹0 :
= =1, .. jº1, Î(-¥;0)È(0;+¥).
= =1, .. m=1.
2) ¹0 :
= =-1, .. yº-1, Î(-¥;0)È(0;+¥).
= =-1, .. n=-1.
.., (0,0) m¹n.
3) , (0,0) .
. "kÎN Mk , ¹(0,0), Mk (0,0) k¥.
: f(M1)=0, f(M2)=0,,f(Mk)=0,. , f(Mk)0, k¥.
"kÎN , ¹(0,0), (0,0) k¥.
: f()= , f()= ,,f()= ,. , f() , k¥.
, .