' : .

#

1 ; R. () f, x e A y. y f x f (). 2 ; f Oxy . M(x,y) y = f(x), M(x,f(x)), x e A , f Cf . 3 ; f, g , : S = f + g, S(x) = (f + g)(x) = f(x) + g(x), x e A D = f - g, D(x) = (f - g)(x) = f(x) - g(x), x e Af P = f g, P(x) = (f g)(x) = f(x) g(x), x e A ff R = , R(x) = gf(x)(x) =, x e A g(x) 0.g(x)v g j . 4 ; f : , x1,x2 e xt < x2 : f(xt) f(x2).

5 ; f : x0 e A () , f(x0) , f(x) < f(xo) x e A x0 e A () , f(x0) , f(x) > f(xo) x e A 6 ; f : x1 e A, f(x) < f (xt) x , x2 e A , f(x) > f (x2) x x2 . , , . 7 x0 ; f x0, lim f(x) = f(x0).x^xo 8 ; f , x0 e A lim f() = f(o).X ^ Xo

9 ; , . , , , , , . 10 xG ; f xG f(xG + h) - f(xG), lim .h^G h f xG f'(xG) . 11 y = f (x) x x = xG; f xG f'(xG) y = f (x) x, x = xG. 12 f ; f , x e A f . , x e B f '(x) = limf(x + h)f(x).h^G h () f f'. 13 f (x) = c f '()= (c)' = G. f (x + h) - f (x) = c - c = G h G, f (x + h)= g ,h lim f (x + h)= G . f '()= (c)' = G .h^Gh 14 f (x) = x f '()= (x)' = 1. f (x + h) - f (x) = (x + h) - x = h, h G, f (x + h)h = j.hh lim f (x + h)= liml = 1. f'( )= (x )' = 1.h^Ghh^G

15 f (x) = x2 f '()= (x2)' = 2x. f (x + h) - f (x) = (x + h)2 - x2 = x2 + 2xh + h2 - x2 = (2x + h)h ,i f (x + h) - f (x) (2x + h)h . , h * 0 , = - = 2 x + h ., lim f (x + h)= lim(2x + h) = 2x. f'()= (x2)' = 2x.h^0 h h^0 16 F (x) = cf (x) :F ()= (c f (x))' = c f'(x). F(x + h) - F(x) = cf (x + h) - cf (x) = c( f (x + h) - f (x)), h*0, F(x + h)-F(x) = c(f(x + h)- f(x) = cf(x + h)- f(x).h h hf (x + h) - f (x)= cf'(x). lim F(x + h) - F(x) = limh^0 h h^0h F ( )= (c f (x))' = c f'(x). 17 F (x) = f (x) + g (x) :F ( )= (f (x) + g(x))' = f'(x) + g'(x). F(x + h) - F(x) = (f (x + h) + g(x + h)) - (f (x) + g(x))= (f (x + h) - f (x)) + (g (x + h) - g (x)), h * 0, F (x + h) - F (x) = f (x + h) - f (x) + g (x + h) - g (x) .h h hlim F(x + h) - F(x) = lim f (x + h) - f(x) + lim g (x + h) - g(x) = f (x) + g (x). h^0hh^0hh^0h F ()= (f (x) + g(x)) ' = f'(x) + g '(x)

18 ; : ( ) ( )iii) .( ). 19 ; . . 20 ; . . . ) ( ).. . ) ( (,)). . . .. (,,.) 21 ; ;: . 10 .: () . . . , , , , , . . 22 ; :) , ( )) , . . 23 ; :) , ,) , ,) (), ,) , , , , . 24 () i xf, ; xl3x2,...,x , , < . () i xf, Xf . , : 1 + 2 +... + = v 25 fi xt, ; ; fi xi vt , Vifi =L, i = 1,2,..., .V :0 < fi < 1 i = 1,2,..., 0 < vi < .f1 + f2 +... + fK = 1, / /r V1 V 2Vk Vj + V2 + ... + Vk Vfi + f2 +... + fK = + +... + = -2 = 1.VVVV 26 . xt, Vi, fi , . , (xi, Vi) (xi, fi), (xt, f %) , . 27 N, Fi, xi, ; : Nt, xi , F , xi . Fi 100 , Ft % = 100F;. x1,x2,. .,x , xt Ni = V1 + V2 +... + Vi., Fi = f1 + f2 + ... + fi, i=1,2,..., . 28 ; . . . 29 ; ; . xf . (xi5 1) (xi5 fi) , , . 30 ; , . , af vf 36G fi xf . 1 = 1= 36Gf1 i = 1,2,..., . 31 ; , . .

32 ; ; . , , . , (), , . c , , . , . . , . 1. 33 ; ; ( ) ( ), , . [, ], , . , .

34 ; , . 35 X ; ( X ) .X = t1 + t2 + + t V = 1 V

ti,t2,tv. t,V -1

x19x2,_,xk v15v2,...,vk .x = x1V 1 + x2V2 + .. + xkVk = I^Tx = xf

V ! v=v1+v2+v3+ .. .+vk.v x; . 36 xj,x2)...,xv wi,w2,...,wv.; 2,2,..., wi,w2,...,wv ^: x,w,

x = x1W1 + x2 W2 + + x VW v = j=1W, + W2 + + W V^-11 2 V w,i=1

37 ; () , , , . 50% 50% . 38 ; . , , . 39 (R) ; (R) = . . 40 t1,t2,...,tv , x. ti -x , t2 -x , t3 -x ,, 1 -x . . (*1 ~ X ) +(*2 ~ X ) + ... + (_ X ) = ?1 + *2 + ... + ~ = *1 + t2 + ... + _ = _ = Q

41 (s2) ;~< rrrr