, .. .
: (, ) - z, z .
z = f(x, y)
: (, ) z, , , .
: z (, ), z .
: 0(0, 0) r (, ), .
: f(x, y) (, ) 0(0, 0), e > 0 r >0, (, ),
.
:
: 0(0, 0) f(x, y). z = f(x, y) 0(0, 0),
(1)
(, ) 0(0, 0) .
(1) , f(x, y). :
1) z = f(x, y) 0(0, 0).
2) .
3) , f(x0, y0).
. f(x, y) D, N(x0, y0,
f(x0, y0) ³ f(x, y)
N1(x1, y1), ,
f(x1, y1) £ f(x, y)
f(x0, y0) = M , f(x1, y1) = m f(x, y) D.
D .
. f(x, y) D, M m , m Î [m, M]
N0(x0, y0) , f(x0, y0) = m.
, D M m. , M m , D .
. f(x, y), D, , , .
, .
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