数值计算课后 课后答案（14）曾喆昭 文卉编著.pdf

? ? ? 2008?02 2008?07 ? 1.?: (1)?x= 22/7 3.14285714, ?x = 3.1415926, ?ea= x x 0.0012645, ?er= ea x 0.00126/3.14159 0.0004025; (2)?x= 3.1416, ?x = 3.1415926, ?ea= x x 0.0000074, ?er= ea x 0.00126/3.1415926 0.000002355; (3)?x= 2.718, ?x = 2.71828, ?ea= x x 0.00028, ?er= ea x 0.00028/2.71828 1.03 104; (4)?x= 1.414, ?x = 2 1.4142, ?ea= x x 0.0002, ?er= ea x 0.0002/1.4142 1.4142 104; (5)?x= 22000, ?x = e10 2.7182810 22026.3176, ?ea= x x 26.3176, ?er= ea x 26.3176/22026.3176 0.00119?er ea x 26.3176/22000 0.001196; (6)?x= 1400, ?x = 10 1385.4557, ?ea= x x 14.5443, ?er= ea x 14.5443/1385.4557 0.0104978?er= ea x 14.5443/1400 0.010389; (7)?x= 39900, ?x = 8! = 40320, ?ea= x x = 420, ?er= ea x = 420/40320 0.0104167; (8)?x= 18(9/e)9 359539, ?x = 9! = 362880, ?ea= x x 3341, ?er= ea x 3341/362880 0.0092. 2.?: 3 ?|ea| |er| x,?x?x |er| x,x + |er| x.? (1) 150-0.001*150,150+0.001*150=149.85,150.15; (2) 900-0.001*900,900+0.001*900=899.1,900.9; (3) 1500-0.001*1500,1500+0.001*1500=1498.5,1501.5; (4) 90-0.001*90,90+0.001*90=89.91,90.09. 3.?: (1)? |e1| |2.7 2.71828| = 0.01828 0.05 = 0.1/2, ?,?2?. ?|er1| = |e1|/e 0.05/2.7 0.0185, ?0.0185.?3?,? ?. ?|er1| = |e1|/e 0.02/2.7 0.00741?0.00741; (2)? |e2| |2.71 2.71828| = 0.00828 0.05 = 0.1/2, ?,?2?. ?|er1| = |e1|/e 0.05/2.71 0.01845, ?0.01845; (3)? |e2| |2.718 2.71828| = 0.00028 0.0005 = 0.001/2, ?,?4?. ?|er1| = |e1|/e 0.0005/2.718 0.0001840, ?0.0001840. 4.?: ?0.5102= 0.01/2,? ?. (1)?,?3?; (2)?,?1?; (3)?(2)?. ?184 105= 0.00184,?,?0? ?. 5.?: 4 ?x1= 22/7 3.1428, x2= 355/113 3.14159292,? ?|e1| 0.0012 0.005 = 0.01/2?|e2| 0.00000032 0.0000005 = 0.000001/2,?,? ?3?7?. 6.?: (1)?|x| 1?, 1 1+2x ? 1x 1+x ?1,? ?,? 1 1 + 2x 1 x 1 + x = 2x2 (1 + 2x)(1 + x); (2)?|x| 1?, cosx?1,?, ? 1 cosx = 2sin2 x 2 ; (3)?|x| 1?, ex?1,?,? ?taylor? ex 1 x + x2 2! + x3 3! + + xn n! . 7.?: ?702 90, 22 3,?(2)?(3)? ?,?. ?(1)?(4)?,?0,?. ?(1)?1?5?1?,?(4)?1? ?1?,?2?1?,?(1)?,? ?(4)?. 8.?: ?x 0 = 1.41?3?,?,? ?|e0| = |x 0 x0| 0.01/2 = 0.005. ?xn= 10 xn1 1,?,x n= 10 xn1 1. ? |en| = |x nxn| = |(10 x n11)(10 xn11)| = 10|10 x n11xn1| = 10|en1|. ? |e10| 10|e9| 102|e8| 1010|e0| = 0.005 1010= 5 107. ?5 107,?. 5 9.?: ?b2 4ac = 562 4 56 = b,?x = bb24ac 2a ?.?: x1= b+b24ac 2a = 56+5624 2 = 28 + 282 1 = 28 + 783 55.982, x2= b a x1= 56 55.982 = 0.018, ? x2= c a/x1 = 1/55.982 = 0.01786. 10.?: ?545.61.?4? 0.5102,?0.51024 = 0.02 0.05 = 0.1/2,? ?,?4?,?545.6. 6 ? 1.?: p2(x)= 0.5 (x2.5)(x4.0) (2.02.5)(2.04.0) + 0.4 (x2.0)(x4.0) (2.52.0)(2.54.0) + 0.25 (x2.0)(x2.5) (4.02.0)(4.02.5) = 1 2(x 2.5)(x 4.0) 8 15(x 2.0)(x 4.0) + 1 12(x 2.0)(x 2.5). ?, f(3) p2(3) = 1 2(3 2.5)(3 4.0) + 8 15(3 2.0)(3 4.0) + 1 12(3 2.0)(3 2.5) = 13 40 = 0.325 2.?: ?xk,xk+1 = kh,(k + 1)h?, lagrange? ? |r1(x)|= e 2!|x xk|x xk+1| e 2h 2 ?|r1(x)| 106,? e 2h 2 106, ? h2 106 2 e 106, ?h 103. 3.?: (1) p1(x)= 2.3979 x12 1112 + 2.4849 x11 1211 = 2.4849(x 11) 2.3979(x 12). ?, ln11.75 p1(11.75) = 2.4849(11.75 11) 2.3979(11.75 12) = 2.46315, 7 ? r1(x) = 1/ 2 2! (x x0)(x x1), ? r1(11.75)= 1 22(11.75 11)(11.75 12), = 3 322 3 32112 7.75 104. (2) p2(x)= 2.3979 (x12)(x13) (1112)(1113) + 2.4849 (x11)(x13) (1211)(1213) + 2.5649 (x11)(x12) (1311)(1312) = 1.19895(x 12)(x 13) 2.4849(x 11)(x 13) + 1.28245(x 11)(x 12). ?, ln11.75p2(11.75) =1.19895(11.75 12)(11.75 13) 2.4849(11.75 11)(11.75 13) +1.28245(11.75 11)(11.75 12) =2.46381, ? r2(x) = 2/ 3 3! (x x0)(x x1)(x x2), ? r2(11.75)= 1 33(11.75 11)(11.75 12)(11.75 13), = 1 643 1 64113 1.1739 105. 4.?: (1)?: 8 ?0?1?2? 112.3979 122.4849 2.48492.3979 1211 = 0.0870 132.5649 2.56492.4849 1312 = 0.0800 0.08000.0870 1311 = 0.0035 (2) newton?: p2(x)= f(x0) + f(x0,x1)(x x0) + f(x0,x1,x2)(x x0)(x x1) = 2.3979 + 0.0870(x 11) 0.0035(x 11)(x 12), (3)?: ln11.75 p2(11.75) = 2.3979+ 0.0870(11.75 11) 0.0035(11.75 11)(11.75 12) = 2.46381, 5.?: ?,?h = 0.1,?newton? ?. (1)?: xkykyk2yk3yk4yk5yk 0.01.00 0.11.320.32 0.21.680.340.04 0.312.0810.4010.0410 0.42.52-9.56-19.36-30-40 0.53.000.4810.043060100 (2)?newton?: p2(x)= y0+ 1 hy0(x x0) + 1 2!h2 2y0(x x0)(x x1) = 1.00 + 10 0.32x+ 50 0.04x(x 0.1) = 1.00 + 3.2x + 2x(x 0.1). ?x = x0+ th = 0.1t,? p2(0.1t)= y0+ ty0+ t(t1) 2! 2y0 = 1.00 + 0.32t + 0.04 2! t(t 1) = 1.00 + 0.32t + 0.02t(t 1). 6.?: 9 (1)?x = 0?2?p(0) = 1,p(0) = 0?1?taylor ?: p(x) = p(0) + p(0)(x 0) = 1 + 0 x = 1. (2)?p(1) = 2 ?.? p(x) = 1 + c(x 0)2= 1 + cx2, ?c?.?p(1) = 2?c = 1,?,? p(x) = 1 + c(x 0)2= 1 + x2. 7.?: ? p3(x)= p(0)0(x) + p(1)1(x) + p(0)0(x) + p(1)1(x) = 1(x) + 0(x) + 21(x), ?1(x),1(x),1(x)?3?,?: 1(0) = 0,1(1) = 1,1(0) = 0,1(1) = 0, 0(0) = 0,0(1) = 0, 0(0) = 1, 0(1) = 0, 1(0) = 0,1(1) = 0, 1(0) = 0, 1(1) = 1, ?1(0) = 1(0) = 0?1(x)?: 1(x) = x2(ax + b), ?1(1) = 1?1(1) = 0? ( a + b = 1, 2(a + b) + a = 0 ?a = 2,b = 3,?1(x) = x2(2x + 3). ?psi0(0) = 0(1) = 0(1) = 0 ?0(x)?: 0(x) = k1x(x 1)2, ? 0(0) = 1 ?k1= 1,?0(x) = x(x 1)2. ?1(0) = 1(1) = 1(0) = 0 ?0(x)?: 0(x) = k2x2(x 1), ? 1(1) = 1 ?k2= 1,?0(x) = x2(x 1). 10 ?, p3(x) = x2(2x + 3) + x(x 1)2+ 2x2(x 1). 8.?: ?p(0) = 1,p(1) = 0,p(0) = 2,p(1) = 10?7? ?(?(3.4-9)?(3.4-10)?3?p3(x),? ? p4(x) = p3(x) + cx2(x 1)2, ?c?.?p(0),p(1)?p(0),p(1)?,? ?0,?p4(x)?4?. ?p(1) = 40?c. 9.?: ?7?,?(3.4-9)?(3.4-10)?. 10.?1: ?(3.5-15)?mi,?(3.5-6)? si(x),?m0= y 0 = 0,mn= y n= 0. ?2? ?: ?x0= 1,x1= 2,x2= 4,x3= 5.?mi= f(xi)(i = 0,1,2,3),? ?m0= m3= 0.(?2?.) (1)?s(x)?: s 1(x) = m0 xx1 x0x1 + m1 xx0 x1x0 = m1(x 1), s 2(x) = m1 xx2 x1x2 + m2 xx1 x2x1 = m1 2 (x 4) + m2 2 (x 2), s 3(x) = m2 xx3 x2x3 + m3 xx2 x3x2 = m2(x 5). (2)?s(x)?s(x): ?1?: s 1(x) = r s 1(x)dx = r m1(x 1)dx = m1 2 (x 1)2+ c11, s 2(x) = r s 2(x)dx = r m1 2 (x 4) + m2 2 (x 2)dx = m1 4 (x 4)2+ m2 4 (x 2)2+ c21, s 3(x) = r s 3(x)dx = r m2(x 5)dx = m2 2 (x 5)2+ c31. 11 ?1?: s1(x)= r m1 2 (x 1)2+ c11dx = m1 6 (x 1)3+ c11x + c12, s2(x)= r m1 4 (x 4)2+ m2 4 (x 2)2+ c21dx = m1 12 (x 4)3+ m2 12 (x 2)3+ c21x + c22, s3(x)= r m2 2 (x 5)2+ c31dx = m2 6 (x 5)3+ c31x + c32. (3)?cij: ?s1(1) = 1,s1(2) = 3?s2(2) = 3,s2(4) = 4?s3(4) = 4,s3(5) = 2? s1(1)= c11+ c12= 1, s1(2)= m1 6 + 2c11+ c12= 3, s2(2)= 8m1 12 + 2c21+ c22= 3, s2(4)= 8m2 12 + 4c21+ c22= 4, s3(4)= m2 6 + 4c31+ c32= 4, s3(5)= 5c31+ c32= 2. ? c11= 2 m1 6 ,c12= 1 + m1 6 ; c21= 1 2 + 1 3(m1 m2),c22= 2 2 3(2m1 m2); c31= 2 + m2 6 ,c32= 12 5m2 6 . (3)? mi?s(x)?s(x): s1(x)= m1 6 (x 1)3+ 2 m1 6 x 1 + m1 6 , s2(x)= m1 12 (x 4)3+ m2 12 (x 2)3+ 1 2 + 1 3(m1 m2)x + 2 2 3(2m1 m2), s3(x)= m2 6 (x 5)3+ 2 + m2 6 x + 12 5m2 6 . 12 ? s 1(x) = m1 2 (x 1)2+ 2 m1 6 , s 2(x) = m1 4 (x 4)2+ m2 4 (x 2)2+ 1 2 + 1 3(m1 m2), s 3(x) = m2 2 (x 5)2 2 + m2 6 . (4)?s(x)?s i(xi) = si+1(xi) ?mi: m1 2 + 2 m1 6 = s 1(2) = s2(2) = m1+ 1 2 + 1 3(m1 m2), m2+ 1 2 + 1 3(m1 m2) = s 2(4) = s3(4) = m2 2 2 + m2 6 . ? m1+ 1 3m2 = 3 2, 1 3m1 + m2= 5 2. ?m1= 3 4,m2 = 9 4. (5)?s(x): s(x) = 1 8(x 1) 3 + 17 8 x 9 8, x 1,2, 1 16(x 4) 3 3 16(x 2) 3 + x + 3 2, x 2,4, 3 8(x 5) 3 19 8 x + 111 8 ,x 4,5. 11.?: ? k01234 xk165123150123141 yk187126172125148 ?n = 5,? 5 p k=0 xk= 702, 5 p k=0 x2 k = 99864 5 p k=0 yk= 758, 5 p k=0 xkyk= 108396 ? ( 99864a+ 702b = 108396, 702a+ 5b = 758 13 ?a = 274/181,b = 11030/181,? y = 274 181x 11030 181 . ?: 12.?: ? k01234 xk00.250.500.751.00 yk1.00001.28401.68472.11702.7183 ?n = 5,? 5 p k=0 xk= 2.5, 5 p k=0 x2 k = 1.875, 5 p k=0 x3 k = 1.5625, 5 p k=0 x4 k = 1.3828125, 5 p k=0 yk= 8.804, 5 p k=0 xkyk= 5.4694, 5 p k=0 x2 kyk = 4.4105375 ? 5a0+ 2.5a1+ 1.875a2= 8.804, 2.5a0+ 1.875a1+ 1.5625a2= 5.4694, 1.875a0+ 1.5625a1+ 1.3828125a2= 4.4105375. ?a0= 1.00205,a1= 0.946469,a2= 0.761371.?,? y = 0.761371x2+ 0.946469x+ 1.00205. 13.?: 14 ?y = aexpbx.?z = g(x) = lny = lna + bx := c + bx,? ? k01234 xk1.001.251.501.752.00 yk5.105.796.537.458.46 zk= lnyk1.629241.756131.876412.008212.13535 ?,n = 5,?: 5 p k=0 xk= 7.5, 5 p k=0 x2 k = 11.875, 5 p k=0 zk 9.40534, 5 p k=0 xkzk 14.42409. ?,?z = g(x)? ( 11.875b+ 7.5c 14.42409, 7.5b + 5c 9.40534 ?b 0.505728,c 1.12248,?a = expc 3.07246,? ?y = aexpbx 3.07246exp0.505728x. 14.?: ?e1= 2x+4y 11,e2= 3x5y 3,e3= x+2y 6,e4= 2x+y 7,? ?e(x,y) = e2 1+ e22+ e23+ e24. ?(x,y)? ?,?e(x,y)?.? e x = 0 = e y, ? ( 2 2(2x + 4y 11) + 2 3(3x 5y 3) + 2(x + 2y 6) + 2 2(2x + y 7) = 0, 2 4(2x + 4y 11) + 2 (5)(3x 5y 3) + 2 2(x + 2y 6) + 2(2x + y 7) = 0, ? ( 18x 3y = 51, 3x + 46y = 48, ?x = 830/273,y = 113/91. 15.?. ? ? ? 2008?02? 2008?07? ? 1.?: ?f(x) = 1?, r1 0 f(x)dx = r1 0 1dx = x|1 0= 1; 2 3f( 1 4) 1 3f( 1 2) + 2 3f( 3 4) = 2 3 1 3 + 2 3 = 1, ?; ?f(x) = x?, r1 0 f(x)dx = r1 0 xdx = 1 2x 2|1 0= 1 2; 2 3f( 1 4) 1 3f( 1 2) + 2 3f( 3 4) = 2 3 1 4 1 3 1 2 + 2 3 3 4 = 1 2, ?; ?f(x) = x2?, r1 0 f(x)dx = r1 0 x2dx = 1 3x 3|1 0= 1 3; 2 3f( 1 4) 1 3f( 1 2) + 2 3f( 3 4) = 2 3 (1 4) 2 1 3 (1 2) 2 + 2 3 (3 4) 2 = 1 3, ?; ?f(x) = x3?, r1 0 f(x)dx = r1 0 x3dx = 1 4x 4|1 0= 1 4; 2 3f( 1 4) 1 3f( 1 2) + 2 3f( 3 4) = 2 3 (1 4) 3 1 3 (1 2) 3 + 2 3 (3 4) 3 = 1 4, ?; ?f(x) = x4?, r1 0 f(x)dx = r1 0 x4dx = 1 5x 5|1 0= 1 5; 2 3f( 1 4) 1 3f( 1 2) + 2 3f( 3 4) = 2 3 (1 4) 4 1 3 (1 2) 4 + 2 3 (3 4) 4 = 37 192, ?.?3. 2.?: (1)?: 3 ?2?1,? ?1?x?,?: a0+ a1= r1 0 1dx = 1, 1 4a0 + 3 4a1 = r1 0 xdx = 1 2, ?a0= a1= 1 2, ? z 1 0 f(x)dx 1 2f( 1 4) + 1 2f( 3 4). (2)?: ?1?x?,?x2?. ?f(x) = x2?, r1 0 x2dx = 1 3, ? 1 2( 1 4) 2 + 1 2( 3 4) 2 = 5 16. ?x2?,?1. (3)?: ?x0= 1 4,x1 = 3 4, ?x0,x1?lagrange? ? l0(x) = xx1 x0x1 = 2(x 3 4); l1(x) = xx0 x1x0 = 2(x 1 4). ?,?: w0= r1 0 l0(x)dx = r1 0 2(x 3 4)dx = (x 3 4) 2|1 0= 1 2 = a0; w1= r1 0 l1(x)dx = r1 0 2(x 1 4)dx = (x 1 4) 2|1 0= 1 2 = a1, ?, (1)?. 3.?: ?,?. (1)?: ?f(x) = 1?, r3 0 f(x)dx = r3 0 1dx = x|3 0= 3; 3 2f(1) + f(2) = 3 21 + 1 = 3, ?; 4 ?f(x) = x?, r3 0 f(x)dx = r3 0 xdx = 1 2x 2|3 0= 9 2; 3 2f(1) + f(2) = 3 21 + 2 = 9 2, ?; ?f(x) = x2?, r3 0 f(x)dx = r3 0 x2dx = 1 3x 3|3 0= 9; 3 2f(1) + f(2) = 3 21 2 + 22 = 15 2 , ?.?1. (2)?: ?,?2?,?1? ?. ?1,?. 4.?: (1)?2?(3)?,?lagrange?,?wi, ?ai= wi?,?. (2)?1? 5.?: ?4?.?.? ?,?(?n+1?,? ?n?),?1,x,x2?(?2?(1). 6.?: ?3?,?2,? ?1,x,x2?. (1)?,? f(x)?x,? ?ha1f(h)+a0f(0)+a1f(h) = hha1+0a0+ha1 = h2a1a1, ?,?x?,? r2h 2hxdx = 0. ?h2a1a1 = 0, ?a1= a1.?,?x3,x5?. (2)?1?x2? ha1+ a0+ a1 = r2h 2h1dx = 4h, h(h)2a1+ 02a0+ h2a1 = r2h 2hx 2dx =16 3 h3, 5 ? a1+ a0+ a1= 4, a1+ a1= 16 3 , ?a1= a1= 8 3,a0 = 4 3. ?,?: z 2h 2h f(x)dx h8 3f(h) 4 3f(0) + 8 3f(h). 7.?: (1)?: ?1,x,x2?,?: 1 a0+ 1 a1+ 1 b0= r1 0 1dx = 1, 0 a0+ 1 a1+ 1 b0= r1 0 xdx = 1 2, 02 a0+ 12 a1+ 2 0 b0= r1 0 x2dx = 1 3, ? a0+ a1= 1, a1+ b0= 1 2, a1= 1 3, ?a0= 2 3,a1 = 1 3,b0 = 1 6, ?: z 1 0 f(x)dx 2 3f(0) + 1 3f(1) + 1 6f (0). (2)?: ?2,?x3?,? ?. ?f(x) = x3?, r1 0 f(x)dx = r1 0 x3dx = 1 4x 4|1 0= 1 4; 2 3f(0) + 1 3f(1) + 1 6f (0) =2 30 3 + 1 31 3 + 1 63 0 2 = 1 3, ?.?2. 6 8.?: ?1,x,x2,x3?,? ha0 1 + a1 1 + h2b0 1+ b1 1 = rh 0 1dx = h, ha0 0 + a1 1 + h2b0 1 + b1 1 = rh 0 xdx = 1 2h 2, ha0 02+ a1 12 + h2b0 2 0 + b1 2 1 = rh 0 x2dx = 1 3h 3, ha0 03+ a1 13 + h2b0 3 02+ b1 3 12 = rh 0 x3dx = 1 4h 4, ? a0+ a1= 1, a1+ hb0+ hb1= 1 2h, a1+ 2hb1= 1 3h 2, a1+ 3hb1= 1 4h 3, ? a0= 1 h2+ 1 2h 3, a1= h2 1 2h 3, b0= 1 2 2 3h + 1 4h 2, b1= 1 4h 2 1 3h, ?,? rh 0 f(x)dxh(1 h2+ 1 2h 3)f(0) + (h2 1 2h 3)f(1) +h2(1 2 2 3h + 1 4h 2)f(0) + (1 4h 2 1 3h)f (1). ?3.?x4?,?h = 1,? a0= 1 2,a1 = 1 2,b0 = 1 12,b1 = 1 12, ?,? z 1 0 f(x)dx 1 2f(0) + 1 2f(1) + 1 12f (0) + 1 12f (1). 7 ?f(x) = x4, r1 0 x4dx = 1 5, ? 1 2f(0) + 1 2f(1) + 1 12f (0) +1 12f (1) =1 20 4 + 1 21 4 + 1 124 0 3 + 1 124 1 3 = 5 6 ?x4?.?3. 9.?: ?x = a+b 2 + ba 2 t, x = a t = 1,x = b t = 1,x = a+b 2 t = 0,?g(t) = f(a+b 2 + ba 2 t),? z b a f(x)dx = z b a f(a + b 2 + b a 2 t)d(a + b 2 + b a 2 t) = b a 2 z 1 1 g(t)dt, ?g(t) = f(x)dx dt = ba 2 f(x),?f(x) = 2 bag (t), ? ba 2 r1 1g(t)dt a0g(1) + a1g(0) + a2g(1) +b0 2 bag (1) + b12 bag (0) + b22 bag (1), ?c1= 2 baa0, c0 = 2 baa1, c1 = 2 baa2, d1 = ( 2 ba) 2b0, d0 = ( 2 ba) 2b1, d1 = ( 2 ba) 2b2, ? r1 1g(t)dt c1g(1) + c0g(0) + c1g(1) + d1g(1) + d0g(0) + d1g(1), ?6?,?5,? ?,?g(x)?x,x3,x5?,? c1+ c1+ d1+ d0+ d1= 0, c1+ c1+ 3d1+ 3d1= 0, c1+ c1+ 5d1+ 5d1= 0, ?c1= c1,d1= d1,d0= 0.? r1 1g(t)dt c1g(1) + c0g(0) + c1g(1) d1g(1) + d1g(1). ?g(x)?1,x2,x4,? c1+ c0+ c1= 2, c1+ c1+ 2d1+ 2d1= 2 3, c1+ c1+ 4d1+ 4d1= 2 5, 8 ? c0= 16 15, c1= 7 15, d1= 1 15, ?g(x)? r1 1g(t)dt 7 15g(1) + 16 15g(0) + 7 15g(1) + 1 15g (1) 1 15g (1). ? a0= ba 2 c1= 7 30(b a), a1= ba 2 c0= 8 15(b a), a2= ba 2 c1= 7 30(b a), b0= (ba)2 4 d1= 1 60(b a) 2, b1= (ba)2 4 d0= 0,b2= (ba)2 4 d1= 1 60(b a) 2, ? rb a f(x)dx 7 30(b a)f(a) + 8 15(b a)f( a+b 2 ) + 7 30(b a)f(b) + 1 60(b a) 2f(a) 1 60(b a) 2f(b). ?g(t)?,?g(t)? ?.?g(t)?5. ?g(t) = t6,t7?. ?g(t) = t6?, r1 1g(t)dt = 2 7, ? 7 15g(1) + 16 15g(0) + 7 15g(1) + 1 15g (1) 1 15g (1) = 7 15 + 7 15 + 1 156 (1) 5 1 156 (1) 5 = 2 15. ?,?5. 10.?: ?3?,?1,x,x2?,?3 ?.? a0 1 + a1 1 = rh h1dx = 2h, a0 (h) + a1x1= rh hxdx = 0, a0 (h)2+ a1x2 1= rh hx 2dx =2 3h 3, 9 ? a0+ a1= 2h, ha0= a1x1, h2a0+ a1x2 1= 2 3h 3, ?2?1?h?3?,? a1(x1+ h) = 2h2, a1x1(h + x1) = 2 3h 3, ?x1= 1 3h, ?ha0= a1x1?a1= 3a0,?a0+ a1= 2h,?a0= 1 2h,a1 = 3 2h, ? z h h f(x)dx 1 2hf(h) + 3 2hf( 1 3h). ?1,x,x2?.?f(x) = x3?, rh hf(x)dx = 0, ? 1 2hf(h)+ 3 2hf( 1 3h) = 1 2h 4 + 1 18h 4 6= 0.?2. 11.?: ?4?,?1,x,x2,x3?,?4? ?: a0 1 + a1 1 + a2 1 = r1 0 1dx = 1, a0 0 + a1x1+ a2 1 = r1 0 xdx = 1 2, a0 02+ a1x2 1+ a2 12= r2 0 xdx = 1 3, a0 03+ a1x3 1+ a2 13= r3 0 xdx = 1 4, ? a0+ a1+ a2= 1, a1x1+ a2= 1 2, a1x2 1+ a2= 1 3, a1x3 1+ a2= 1 4, 10 ?2?3?,?3?4?,? a1x1(1 x1) = 1 6, a1x2 1(1 x1) = 1 12, ?a16= 0,x16= 0,1 x16= 0,?x1= 1 2, ? ?a0,a1,a2?,?a0= 1 6,a1 = 2 3,a2 = 1 6, ? ?simpson?,?3. 12.?: ?f(x) = 1?a = 2 3. ?x,x2,x3? x0+ x1+ x2= 0, x2 0+ x21+ x22= 1, x3 0+ x31+ x32= 0, ?x0+ x1+ x2= 0?x0 x1 0,?x1= 0?x1+ x2= 0. ?x1+x2= 0, ?x0+x1+x2= 0?x0= 0,?x0 0?.? ?x1= 0,?x0= x2,?x2 0+x21+x22= 1 ?x0= 2 2 ,x2= 2 2 . ?, z 1 1 f(x)dx 2 3f( 2 2 ) + f(0) + f( 2 2 ). ?f(x) = x4,? r1 1f(x)dx = 1 5, 2 3f( 2 2 ) + f(0) + f( 2 2 ) = 2 3, ? ?3. ?: 16,17,19,20?,? ?. 13.?: 11 ?2?,?1,x?,?2?: a0 1 = r1 11dx = 2, a0 x0= r1