Методические указания к выполнению расчетно-графической и курсовой работы (1013347), страница 2

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.– Z-,:<.R = 3./:/::::5:<Z$/93=13+5/./r2 =:<3;3x1 ;x2/3«"#»%&.•..19$:Z2-:Z3–(Z;•$$5:/;/-1-1/311/3,;)/3:< :(-1),3:$5/1-2,1-12-1-1010111/32/31100Cjx1010x2100x32/3-1/3-1x41/31/30ri0-1/31/33Ci11Ex2 = 2x1 = 122 $3=04=09x2x1,921:<3:x3 = 0x4 = 0x1 , x 2 /$-1111(1, 2) .:2/3= 0 ( 2 / 3 1 / 3) = 1 / 31/ 31/ 3= 0 (1 / 3 + 1 / 3) = 2 / 31/ 36. .-3,,x1* = 1x2* = 2x3* = 0x4* = 0G00,2* (-1)5;431– /Z1-:1:<0315:- 1-$:<&,–/$«5:A = (1, 2) ."#»%&...20".E5$ :f (X) = x 1 + x 2min- x1 + x 2 $ 12 x1 + x 2 $ 4x1 , x 2 % 0#$,/,:(-1),$:f (X) = - x 1 - x 2max- x1 + x 2 $ 12 x1 + x 2 $ 4x1 , x 2 % 06.

.$5$55,$/,$:f (X) = - x 1 - x 2 + 0 x 3 + 0 x 4max- x1 + x 2 + 1 x 3 + 0 x 4 = 12 x1 + x 2 + 0 x 3 + 1 x 4 = 4x1 , x 2 , x 3 , x 4 % 0E" $$ :5:x2 = 0x1 , x 2 /x1 = 0242 $$- x3 ,- x4$x3 = 1x4 = 4$(0, 0) .1Ci00E12-x3 =1x4 = 49x3x5,914x1 = 0x2 = 0-1-100Cjx1-12-1x211-1x3100x4010ri14:<1:-:«"#»%&.1= 12= 1.0000.211= 1 (0 + 0) = 121= 1 (0 + 0) = 116. .-1x1* = 0x2* = 0x 3* = 1x4* = 4G,,–/$«5:O = (0, 0) ."#»%&...224.:*2 x1x15 x110 x1++3 x22 x23 x22 x2"- 4 x3- 5 x3+ x3- x3+ x4 =+ x4 =- 4 x4 =+ 2 x4 =!%"2-5-113:#2 x1x15 x110 x1:++3 x22 x23 x22 x23$- 4 x3- 5 x3+ x3- x32-5-113|2 |<|| -2 | < ||1 |<||2 |<|31510|+||+||+||+|-4 | + |-5 | + |-3 | + |2 |+|1 |1 |-4 |-1 |,,55,/5:3:.$5++3 x22 x23 x22 x22- 4 x3- 5 x3+ x3- x3B5+ x4 =+ x4 =- 4 x4 =+ 2 x4 =2-5-113:/A, B, C, D.

".D/:<:/,$:10 x1 + 2 x 2 - x 3 + 2 x 4 = 13 D---------------------------x1 - 2 x 2 - 5 x 3 + x 4 = -5B---------------------------B5:10 x1 + 2 x 2 - x 3 + 2 x 4 = 13x1 + 5 x 2 + x 3=7x1 - 2 x 2 - 5 x 3 + x 4 = -53 x1- 9 x 4 = -5$ABCD,5“: ”.#,2 x1x15 x110 x1+ x4 =+ x4 =- 4 x4 =+ 2 x4 =DA-BB2A-B+2C-D«"#»%&5/...23#$10 x1 + 2 x 2 - x 3 + 2 x 4 =x1 + 5 x 2 + x 3=x1 - 2 x 2 - 5 x 3 + x 4 =3 x1- 9 x4 =137-5-5N!| 10 | > ||5 |>|| -5 | > || -9 | > |2113|+||+||+||+|-1 | + |1 |+|-2 | + |0 |+|2010:||||.:, /:$- x2: x1 ,,. .13107x2 =5111x4x2 +x3510511x1x355121x 3 = 1 + x1x2 + x455511x 4 = + x163x1 =«"#»%&/..)..24*2$$5,:<)$:13107x 02 =50x3 = 11x 04 =6x10 =+1!$1 01 01 0x4x2 +x351051 01 0x3x15512 01x 13 = 1 + x 10x 2 + x 0455511x 14 = + x 1063,:13x 11 =107x 12 =52 $,:1 711 1+= 0.98715 5105 61 1311 = 0.9405 1051 132 71 1+= 0.833x 13 = 1 +5 105 55 611 13= 1.100x 14 = +63 1013x 11 =107x 12 =5X = max x i02 $ix 1ix10x11 = | 1.3 - 0.987 | = 0.313x 02x 12 = | 1.4 - 0.940 | = 0.460x 30x 13 = | 1.0 - 0.833 | = 0.167x 04x 14 = | 0.667 - 1.1 | = 0.4332$$5X = 0.46,5$.«"#»%&.+..252!$1 11 11 1x4x2 +x351051 11 1x3x15512 11x 32 = 1 + x 11x 2 + x 1455511x 24 = + x 1163,:13x 12 =107x 22 =52 $,110.940 +0.833510110.833 =0.9875512x 32 = 1 +0.9870.940 +55110.987 = 0.996x 24 = +6313x 12 =107x 22 =5X = max x 1i2 $i:11.100 = 0.97551.03611.100 = 1.0415x i2x 11x 12x 12x 22 = | 0.940- 1.036| = 0.096x 13x 32 = | 0.833 - 1.041 | = 0.208x 14x 24 = | 1.100 - 0.996 | = 0.104#= | 0.987- 0.975| = 0.012X = 0.208:<.x10123452 $!x21.3000.9870.9750.9981.0000.999$$x31.4000.9401.0360.9971.0041.000, .

.x41.0000.8331.0410.9780.9990.998$X0.6671.1000.9960.9920.9991.0005 0.01.:x1* = 0.999 1x *3 = 1x *3 = 0.998 1x *4 = 1«"#»%&0.4600.2080.0630.0210.004..)..26*2-$$5,:<$:13107x 02 =5x 30 = 11x 04 =6x10 =+1!$1 01 01 0x4x2 +x351051 11 0x3x15512 11x 13 = 1 + x 11x 2 + x 0455511x 14 = + x 1163,:13x 11 =107x 12 =52 $,:1 711 1+= 0.98715 5105 6111 = 1.0030.98755121 1= 0.930x 13 = 1 +0.9871.003 +555 6110.987 = 0.996x 14 = +6313x 11 =107x 12 =5X = max x i02 $ix 1ix10x11x 02x 12 = | 1.4 - 1.003 | = 0.397x 30x 13 = | 1.0 - 0.930 | = 0.070x 04x 14 = | 0.667 - 0.996 | = 0.329= | 1.3 - 0.987 | = 0.313X = 0.397«"#»%&.+..272!$1 11 11 1x4x2 +x351051 21 1x3x15512 21x 32 = 1 + x 12x 2 + x 1455511x 24 = + x 1263,:13x 12 =107x 22 =52 $,:13107x 22 =51110.996 = 0.9931.003 +0.9305105110.930 = 1.0150.993551210.996 = 0.992x 32 = 1 +0.9931.003 +555110.993 = 0.998x 24 = +63x 12 =X = max x 1i2 $ix i2x 11x 12x 12x 22 = | 1.003- 1.015| = 0.012x 13x 32 = | 0.930 - 0.992 | = 0.062x 14x 24 = | 0.996 - 0.998 | = 0.002#= | 0.987- 0.993| = 0.006X = 0.062:<.x1012342 $!x21.3000.9870.9930.9970.999$$x31.4001.0031.0151.0021.000, .

.x41.0000.9300.9920.9980.999$X0.6670.9960.9980.9980.9995 0.01.:x1* = 0.999 1x *3 = 1x *3 = 0.999 1x *4 = 0.999 1«"#»%&0.3970.0620.0130.002...285.x3:!11x 2 + 36x%!36 = 0:)7&!%#."$f &( x ) = 3x 222 x + 36 = 02 $$(;f ( x 1 ) = 0.8794!,$22 ± 22 2 4326$$ :x1(;, 2 =5:x 1(; = 2.4648 x (;2 = 4.8685f ( x (;2 ) = 6.0646«"#»%&:...29[ x 1(; , x (;2 ]6. .([2.5, 4.7] ' (2.4648, 4.8685)3b = 2.3 < 2.4648 ,a = 1 .6 .5.

2$3$)8:$$&*%(& %)0.01(6; #). 2b&"5:,11x 2 + 36x2 $0$$5$,:211 1.6 + 36 1.6 36= 1.89057x 1 = 1.6 1.89057 = 0.29062 $x 2 = x1x13f (x )= 1.89057f &( x1 ),:31.89057 11 1.89057 2 + 36 1.89057 363 1.89057 2 22 1.89057 + 36= 1.98782x 2 = 1.89057 1.9878 = 0.0972«"#5$36f (x )1.6=1.6f &( x 0 )3 1.6 2 22 1.6 + 3615.&).&)x05x 0 = 1.6,f &( x ) = 3x 2 22x + 36f &&( x ) = 6 x 22, $:: f (1.6) f &&(1.6) > 0 .x1 = x 0$[1.6; 2.3][2.5; 4.7][4.9; 7.1]$#"5:5(-#; 2). 2$$ ,:f (x ) = x 35$:5B,,$&[1.6; 2.3],$5$5 :5 x1 = 25 x2 = 35 x3 = 6%2),5 x3 = 6 .

23a = 4.9 > 4.8685 ,b = 7 .1 .,»%&5:.#..30:<.x012342 $#$)8$%1.61.89061.98781.99982.0000&*&$()x3#2 5#"(x3)5 0.01.&x=x+11x 2 + 36xf (x) ,36 = 0%& %:<0.01:11x + 36 x 36)= 0 .2 ,( x ) = x 0.2 ( x 3 11x 2 + 36 x 36)5.&( x ):[1.6; 2.3].22 x + 36)),$O0.29060.09720.01200.00022&( x ) = 1 0.2(3x 2#x-2.464-0.4989-0.0495-0.00070.0000, . .x * = 2.&[1.6; 2.3],x=x+f(x):(x)&( x ) < 1,[1.6; 2.3].5/.«"#»%&..2.31$2 $x1 =x050( x ) = 1 .6x 0 = 1.6 .,,0 .

2 (1 . 6 3:11 1 . 6 + 36 1 . 6236 ) = 2 . 09281x = 1.6 2.0928 = 0.49282 $,:213x = ( x ) = 2.0928 0.2( 2.0928 11 2.0928 2 + 36 2.0928 36) = 2.02701x1 x 2 = 2.0928 2.02701 = 0.06579#:<:x012345#!) 81.62.092802.027012.006132.001262.00025x * = 2.00025$%&(x)f(x)2.092802.027012.006132.001262.000252.00005x-2.464000.328940.104420.024320.005040.001020.492800.065790.020880.004860.001010.000202.&*([1.6; 2.3],%)&& %!0.03#[1.6; 2.3]:f (1.6) = 2.464f (1.6) f (2.3) < 0 -f (2.3) = 0.777$.!(")12 $$f(a) = f(1.6) = -2.464 ,<f(b) = f(2.3) = 0.777a + b 1.6 + 2.3<c=== 1.9522: f(c) = f(1.95) = -0.2126"2 $;f(a) < 0[1.6; 2.3]:$f (a) f (c) , /f(c) < 0,$x = 2.3 1.6 = 0.7 /, :,5[c, b] = [1.95; 2.3]$:$5 0.03 ,.22 $$f(a) = f(1.95) = -0.2126,<[1.95; 2.3]:f(b) = f(2.3) = 0.777«"#»%&$, .

....32"c=<2 $;f(a) < 0$f (a) f (c) , /, :$:$5 0.03 ,$.:<:0123452 $#$,5, . .[a, c] = [1.95; 2.125]$f(c) > 0,x = 2.3 1.95 = 0.35 /#a + b 1.95 + 2.3== 2.12522: f(c) = f(2.125) = 0.4238$abf(a)1.61.951.951.951.99381.99382.32.32.1252.03752.03752.0156-2.464-0.2126-0.2126-0.2126-0.0252-0.0252, . .x = 2.0047*f(b)c=0.7770.7770.42380.14300.14300.0613$a+b21.952.1252.03751.99382.01562.00475 0.03.2.«"#»%&f( ()-0.21260.42380.1430-0.02520.06130.0186x0.70.350.1750.08750.04380.0219...336.

;"%:11xy = f (x )2103241:)&L(x) =1 !(x 1)(x 2)(x 3)(x 1)(x 3)(x 4)(x 1)(x 2)(x 4)(x 2)(x 3)(x 4)12 +1+10 +(4 1)(4 2)(4 3)(2 1)(2 3)(2 4)(3 1)(3 2)(3 4)(1 2)(1 3)(1 4);:x3 9x2 + 26x 24x3 8x2 +19x 12x3 7x2 +14x 8x3 6x2 +11x 6L(x) =+10 +2 +6226L(x) = 4x 3 32.5x 2 + 78.5x 49)&)#$y 0 = y1y0y1 = y 2y2 = y3y1y2$0123#55.&),2y 0 = y12xy = f (x )123411021y1 = y 2y5y0533y-177,2y0 =y1y129-8-1:y24:"5::22y0y0y0(x x 0 )(x x1 )(x x 2 ) ,+P(x) =(x x 0 ) +(x x 0 )(x x1 ) +023h 1!h 0!h 2!h 3!h = x1 x 0y0P(x) =;101 0!+91724(x 1)(x 2)(x 3)(x 1) +(x 1)(x 2) +231 1!1 2!1 3!:P( x ) = 1 + 9( x 1) 8.5( x 23x + 2) + 4( x 3«6x 2 + 11x"6)#»%&2y0...34P(x) = 4x 3 32.5x 2 + 78.5x 49)$&)1-!2-!&* "E5":<22g 2 (x ) = a 2 x + a 1x + a 0a 0 , a1 , a 2/$:::s 0 a 0 + s1 a 1 + s 2 a 2 = t 0s 1a 0 + s 2 a 1 + s 3 a 2 = t 1s 2 a 0 + s 3a1 + s 4 a 2 = t 2:<1g1 (x ) = a 1 x + a 0a 0 , a1:0"/5:$:s 0 a 0 + s1 a 1 = t 0#s 0 = x 00 + x 10 + x 02 + x 30s 1a 0 + s 2 a 1 = t 1::1s1 = x 0 + x 11 + x 12 + x 13s 2 = x 02 + x 12 + x 22 + x 32s 3 = x 30 + x 13 + x 32 + x 33s 4 = x 04 + x 14 + x 42 + x 34t 0 = y 0 x 00 + y1 x 10 + y 2 x 02 + y 3 x 30t 1 = y 0 x 10 + y1 x 11 + y 2 x 12 + y 3 x 13t 2 = y 0 x 02 + y1 x 12 + y 2 x 22 + y 3 x 32B/:<:$0123(x0x1x2x3x4y x0y x1y x211111234149161827641168125611021120641401816s0s1s2s3s4t0t1t241030100354143175!/:<:«"#»%&2-...354a 0 + 10a 1 + 20a 2 = 1410a 0 + 30a 1 + 100a 2 = 3130a 0 + 100a 1 + 354a 2 = 75"A410:30= 10 30 100 = 80 ,30 100 35414110304= 31 30 100 = 560 ,75 100 3546$a0 =13024= 10 31 100 = 936 ,30 750 354/560= 7 , a1 =80=21431014= 10 30 31 = 20030 100 75:=936= 11.7 , a 2 =803=200= 2 .580g 2 (x) = 2.5x 2 + 11.7x 7G$,1-/:<:4a 0 + 10a 1 = 1410a 0 + 30a 1 = 31"A=4 10= 20 ,10 306a0 =1=14 10= 110 ,31 30$1=110= 5 .5 ,20:2/a1 =2=4 14= 16 ,10 31:=16= 0 .820g1 (x) = 0.8x + 5.5" $,,?:<g1 ( x )«",L( x )g 2 (x) .#»%&"5:P( x ) ,...36«"#»%&...37:"%: a 1 x 12 + a 3 x 22 + a 4 x 1 + a 5 x 2 + a 6 = CB: D=+D>0 D<0 D=0 -OOO____________________________________________________A$/>3/: $: x1 = a, x 2 = b$/2( x 2 b)x1 = a,=1B(x1 a ) 2x 2 = b,=1AB5$+5a) 2(x 1:A(a , b )+6 $$:$+5$:$!A3 56 $x 2 = b,= 1,BA > 0, B > 0X1a , X a2 -$$/5: x 1 = aX1b , X b2 -$$/5: x 2 = b$/, <x2,:,: x1 = ±x1$x1 ,1( x 2 b) 2B, <( x1 a ) 21A$X1a , X a2 ,$X1b , X b2 ,A +a,: x2 = ±x2B+b_________________________________________________$$b) 2(x 2:a) 2(x 1: (1)b) 2(x 2A(2)00a3/'/a10B= 1,A > 0, B > 0( x 1 a ) 2 ( x 2 b) 2+= 1,ABA > 0, B > 0(1): x2 = b$(x1 a ) 2=1A5::X1b , X b2 -$«5: x 2 = b$"#»%&..BB.3855$0:$$$:x1 ,$, <,: x2 = ±x2X1b , X b2 ,$(x1 a ) 21 B+bA(2): x1 = a3 56 $$( x 2 b) 2=1B5$5$x1 = a,BB$:5::X1a , X a2 -$5: x 1 = a$:x2,$, <,: x1 = ±x1X1a , X a2 ,$( x 2 b) 21 A +aB__________________________________________________A$x 2 = Ax12 + Bx1 + C: (1)(2) x 1 = Ax 22 + Bx 2 + C0$(1)2:2B, x *2 = Ax1* + Bx *1 + C2A: x 1 = x 1*:A>0 A<0 -3 52BB55$$55,55x2x2:x1 ,, <$:$: x 2 = Ax12 + Bx1 + Cx20x *1 =$(2): x *2 =2: x 2 = x *2:A>0 A<0 -3 52BB55$2B, x 1* = Ax *2 + Bx *2 + C2Ax155,$55x1x1:$x2,, <$: x 1 = Ax 22 + Bx 2 + C«"#»%&:.

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