f(x), a, a, = f(a). (1)
d- , f(a).
(1) :
. f (x) =, .
. =, { xn } a, { f(xn) } f(a)
D =- , D =f(x)-f(a)=f(a+ D )-f(a) , D . (1) .
. =, , .. =0.
. ( -d, ] f(a-0)=f(a), . , Î[ a,a+d) = f(a).
= f(x), a, , .
: 1) aÎD(f); 2) = ; 3) f(a)=, f(x).
= f (x) f(a-0), f(a+0). = . , h = f(a+ 0 ) - f(a- 0 )¹ 0, . f(a-0)=f(a+0) ( f(a-0)=f(a+0)=f(a), ).
( ) f(a-0), f(a+0) , = .
, :
1) : ($d>0)($c>0):(" ½ f(x) ½£c);
2) f(x) = f(a)¹0, d- , f(a), .. ($d>0):(" f(x)×f(a) >0).
3) f(x), g(x) =, f(x) g(x), f(x)× g(x), f(x)/ g(x) (g() ¹0).
4) z= g(y) y0, y= f(x) x0 (y 0= f(x0)), x0 g(f(x)), 0
: = .
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