!! ## $! $! %% "" & ' ())* ## + $! $! %% ,, .. f(x ) ∈ C2 ([ a, b ]) 0 -1 5 2 ' &34 + ,-. / ) -) / ,-1 $ %.' " h2 0 = f(x*) = f(x 0 + h) = f(x 0 ) + h.f '(x 0 ) + .f "(x 0 + θ.h) 2 + θ ∈ [0,1] %" h2 θ ∈ [0,1] 0 = f(x 0 ) + h.f '(x 0 ) + .f "(x 0 + θ.h) 2 0 " -1 / -) 6 % ( ## ' ' $! $! %% ,(. ,(. " h2 0 = f(x 0 ) + h.f '(x 0 ) + .f "(x 0 + θ.h) 2 θ ∈ [0,1] 8 " 9. θ (9. : 7 ## < " : < : = ! : $! $! %% <> ,7. ,7. > ? h2 0 = f(x 0 ) + h.f '(x 0 ) + .f "(x 0 + θ.h) 2 0 = f(x 0 ) + H.f '(x 0 ) H=− f(x 0 ) f '(x 0 ) (H : h) x * ≈ x1 = x 0 + H = x 0 − f(x 0 ) f '(x 0 ) ; ## $! $! %% ,;. ,;. < 8 -) / A & ' (' 44444 f(xi−1 ) x i = x i −1 − f '(xi−1 ) 4 α f(x 0 ) tg(α α ) = f’(x0) = H f(x 0 ) H= f '(x 0 ) x2 x1 H f(x0) x0 @ ## $! $! %% ,@. ,@. 4444 C< 8 D C > D C < 8 - D ...... B ## : f(x ) g(x ) = x − f '(x ) f(xi−1 ) x i = x i −1 − f '(xi−1 ) $! $! %% ,B ,B.. & " - / ,- $ . EEE : : &G 8 H ,-. &G 8 2 ' &3 |g’(x)| < 1 ' I,-. f "(x ) ⋅ f(x ) <1 f '(x) FFF ,-. 0 2 ' &34 " ∀x ∈ [a, b ] * ## $! $! %% H 5 & + f(x ) ∈ C2 ([ a, b ]) ' f(xi ) x i+1 = x i − f '(xi ) x 0 ∈ [ a,b ] ,* ,*.. ∞ 0 2 ' &3 ' < 5 H 2 ' &3 >< + 8 i= 0 % ,-. / ) G 2 ' &34 & - ' 4 J ## + ,-. / - K , ,-. L # $! % $! $! %% ,J ,J.. I,-. .' ' % 0 - -1 ,-. / ) M- K - $ M + ! ,-. % H # , % % K .4 % G 4 ## ¿ |f(xi)| < ε ? N & 8 M ,- .M O ε $! $! %% ,, .. & M- K - $ M O δ f(x) = x.e-x ε M ,- . M & N & 8 & )) ## : $! $! %% 0 & ,, ). ). " ,-. I,-. < G % G ' % ' ) ## $! $! %% "" I,-. ,-. - ' ' ε - ) - δ (4 O < 5 ! + ,, N >< ! " 9. 0 - $ ,-. L I,-. 79. M , -.M R >:< >H . P ,, - Q ε. H , (9. - ;9. - @9. A (4 Q δ.. M - K 0 M 0 6 > H :4 )( ## $! $! %% "" <<WW : % S " U ( > > A −n Q = . 1 − (1 + i ) i , , T" ) . . ' ' G > % 99 ,, .. , G 8 U / @)))) ' V '444. & ' / @;)) 0 () V (n = 40) )7 ( ## ) $! $! %% "" <<WW 99 ,(. ,(. A −n 5400 Q = . 1 − (1 + i ) 150000 = . ( 1 − (1 + i)−40 ) i i 5400 150000 − . ( 1 − (1 + i)−40 ) = 0 i 5400 1 f(i) f '(i) = . . ( 1 − (1 + i)−40 ) − 40.(1 + i)−41 i i f(ik −1 ) ik = ik −1 − f '(ik −1 ) 5400 150000 − . ( 1 − (1 + ik −1 )−40 ) ik −1 ik = ik −1 − 5400 1 . . ( 1 − (1 + ik −1 )−40 ) − 40.(1 + ik −1 )−41 ik −1 ik −1 ); ## i0 = 0.03 $! $! %% i1 = 0.0175 i3 = 0.0191 "" <<WW 99 ,7. ,7. i2 = 0.0190 i4 = 0.0191 & 4 X 4 H5 " i0 = 3 H >H i1 = -244.000 Y <!Z <4 i2 = - 1654265.777 ,< 4 4" [ .... . )@ ## $! $! %% "" <<WW ' λ' < (9 (9 ,, .. & \' ' 8 ! G ,! . λ −1/ 2 = −2.ln & > & ]" 2.51 K + Re⋅ λ 1/ 2 3.71⋅ D 8 \ / )4)))(@ G ' ! / )47 ' 8 % ! / (4 )@ )B ## λ −1/ 2 $! $! %% "" <<WW (9 (9 ,(. ,(. 2.51 K = −2.ln + 1/ 2 3.71⋅ D Re⋅ λ ,+ λ −1/ 2 = −2.ln . 2.51 0.00025 + = 5 1/ 2 3.71⋅ 0.3 2 ⋅ 10 ⋅ λ 1.255 ⋅ 10 −5 −4 2.24618 10 = −2.ln + ⋅ λ 1/ 2 ,: - / λ$ L(. x = −2.ln ( 1.255 ⋅ 10 −5 ⋅ x + 2.24618 ⋅ 10 −4 ) )* ## $! $! %% "" <<WW (9 (9 ,7. ,7. x = −2.ln ( 1.255 ⋅ 10 −5 ⋅ x + 2.24618 ⋅ 10 −4 ) ,: / x = −2.ln ( a ⋅ x + b ) 4(@@ 4 )$@ e = ( a.x + b ) x & / (4(;B J 4 )$;. −2 f(x) e ⋅ ( a.x + b ) = 1 e ⋅ ( a.x + b ) − 1 = 0 2 x x 2 f '(x ) = e ⋅ ( a.x + b ) + 2.a.e x ⋅ ( a.x + b ) x 2 f '(x ) = e x ⋅ ( a.x + b ) . ( a.x + b + 2.a ) )J ## $! $! %% "" <<WW (9 (9 ,;. ,;. e ⋅ ( a.xi + b ) − 1 2 xi f(xi ) x i+1 = x i − f '(xi ) x i+1 = x i − e ⋅ ( a.xi + b ) − 1 2 xi e xi ⋅ ( a.xi + b ) . ( a.xi + b + 2.a ) e xi ⋅ ( a.xi + b ) . ( a.xi + b + 2.a ) x i+1 = x i − ( a.xi + b ) − e − xi 2 ( a.xi + b ) . ( a.xi + b + 2.a ) ( a = 1.255 .10-5 y b = 2.24618 .10-4) xi +1 = xi − (1.255 ⋅ 10 (1.255 ⋅ 10 −5 −5 .xi + 2.24618 ⋅ 10 ) −4 2 − e − xi g(xi) .xi + 2.24618 ⋅ 10 −4 ) . (1.255 ⋅ 10 −5 .xi + 2.49718 ⋅ 10 −4 ) ) ## $! $! %% "" <<WW (9 (9 ,@. ,@. S T (1.255 ⋅ 10−5.x + 2.24618 ⋅ 10−4 ) − e− x 2 g(x ) = x − (1.255 ⋅ 10 −5 .x + 2.24618 ⋅ 10 −4 ) . (1.255 ⋅ 10 −5 .x + 2.49718 ⋅ 10 −4 ) g(0) = 1.7828121.107 > 0 ( | g’(x) | >>> 1 ) g(1) = 5.914310615.106 > 1 ( | g’(x) | >> 1 ) g(10) = 354. 6536402 > 10 g(20) = 19. 05878 < 20 , + g(20.5) = 19. 55462453 < 20.5 0 & 0 . g(20.5) − g(20) <1 0.5 -) / () ) ## x0 = 20 x1 = 19.05878285 x2 = 18.13341977 x3 = 17.24775965 x4 = 16.45875644 x5 = 15.87532000 $! $! %% "" <<WW | x0 – x1 | = 0.9412... | x1 – x2 | = 0.9253... | x2 – x3 | = 0.8856... | x3 – x4 | = 0.7890... | x4 – x5 | = 0.5834... (9 (9 ,B ,B.. f(x1) = 39.17... f(x2) = 14.34... f(x3) = 5.020... f(x4) = 1.6136... f(x5) = 0.4092... ## x5 = 15.87532000 x6 = 15.60114244 x7 = 15.55279476 x8 = 15.55151517 x9 = 15.55151430 $! $! %% "" <<WW | x5 – x6 | = 0.2741... | x6 – x7 | = 0.0483... | x7 – x8 | = 0.0012... | x8 – x9 | = 8.7.10-7 (9 (9 ,* ,*.. f(x5) = 0.4092... f(x6) = 0.0540... f(x7) = 0.0013... f(x8) = 9.1.10-7 f(x9) = 4.0.10-9 ( ## $! $! %% "" <<WW (9 (9 ,J ,J.. x* ≈ x 9 = 15.55151430 x = λ −1/ 2 λ* = λ= 1 x2 1 1 ≈ = 0.004134801184 2 2 (x*) (15.55151430) > / )4)); 7;444 7 ;