Đáp án đề kiểm tra giua ky Môn Phương pháp tính Học kỳ 1, mã môn HMO2201 Số tín chỉ: 3, Thời gian làm bài 60 phút Đề số 1 Cau 1: tim nghiem lon nhat cua ham so y=f(x)=0 voi sai so 1e-5 y = exp(x.^3) - 5*x.^3 - 30; Loi giai: Ham so exp(x^3) - 5*x^3 - 30 lien tuc tren toan mien. Ham co dao ham: y' = 3*x^2*exp(x^3) - 15*x^2. Dao ham co nghiem tai cac diem: 1.17190. Bang Khao sat ham so exp(x^3) - 5*x^3 - 30. x -Inf -2.00000 -1.00000 1.17190 1.17191 2.00000 Inf y' - - - 0 + + + y Inf 10.0003354626279020 -24.6321205588285572 -33.0471895621705016 -33.0471895579266359 2910.9579870417283018 Inf Ham co nghiem trong cac khoang: ( -2.00000 -1.00000 ), ( 2.00000 1.17191 ) Cach 1: Giai ham y = exp(x^3) - 5*x^3 - 30 bang phuong phap chia doi cho khoang nghiem ( a ; b )=( -2 ; -1 ) buoc a Nghiem x b f(a) f(x) Sai so 1 -2.00000 -1.50000 -1.00000 10.00034 -13.09078 0.50000 2 -2.00000 -1.75000 -1.50000 10.00034 -3.19842 0.25000 3 -2.00000 -1.87500 -1.75000 10.00034 2.96036 0.12500 4 -1.87500 -1.81250 -1.75000 2.96036 -0.22568 0.06250 5 -1.87500 -1.84375 -1.81250 2.96036 1.34025 0.03125 6 -1.84375 -1.82812 -1.81250 1.34025 0.55056 0.01562 7 -1.82812 -1.82031 -1.81250 0.55056 0.16077 0.00781 8 -1.82031 -1.81641 -1.81250 0.16077 -0.03287 0.00391 9 -1.82031 -1.81836 -1.81641 0.16077 0.06385 0.00195 10 -1.81836 -1.81738 -1.81641 0.06385 0.01546 0.00098 11 -1.81738 -1.81689 -1.81641 0.01546 -0.00871 0.00049 12 -1.81738 -1.81714 -1.81689 0.01546 0.00337 0.00024 13 -1.81714 -1.81702 -1.81689 0.00337 -0.00267 0.00012 14 -1.81714 -1.81708 -1.81702 0.00337 0.00035 0.00006 15 -1.81708 -1.81705 -1.81702 0.00035 -0.00116 0.00003 16 -1.81708 -1.81706 -1.81705 0.00035 -0.00040 0.00002 17 -1.81708 -1.81707 -1.81706 0.00035 -0.00003 0.00001 Nghiem cua ham so trong khoang ( -2.000000 ; -1.000000 ) la: -1.81707 +- 0.00001 Cach 2: Giai ham y = exp(x^3) - 5*x^3 - 30 bang phuong phap tiep tuyen trong khoang nghiem ( -2 ; -1 ) Chon nghiem ban dau x0 = -2.00000 buoc Nghiem x f(x) f'(x) Sai so 1 -2.00000 10.00034 -59.99597 0.16668 1 -1.83332 0.81145 -50.39449 0.01610 2 -1.81721 0.00713 -49.50950 0.00014 3 -1.81707053 0.00000057 -49.50161494 0.00000001 Nghiem cua ham so trong khoang ( -2.000000 ; -1.000000 ) la: -1.81707052 +- 0.00000001 Cach 3: Giai ham y = exp(x^3) - 5*x^3 - 30 bang phuong phap day cung trong khoang nghiem ( a; b ) = ( -2 ; -1 ) buoc a x b f(a) f(x) f(b) Sai so 1 -2.00000 -1.71124 -1.00000 10.00034 -4.93769 -24.63212 0.28876 2 -2.00000 -1.80669 -1.71124 10.00034 -0.51088 -4.93769 0.09545 3 -2.00000 -1.81609 -1.80669 10.00034 -0.04870 -0.51088 0.00940 4 -2.00000 -1.81698 -1.81609 10.00034 -0.00461 -0.04870 0.00089 5 -2.00000 -1.81706 -1.81698 10.00034 -0.00044 -0.00461 0.00008 6 -2.000000 -1.817070 -1.817062 10.000335 -0.000041 -0.000435 0.000008 Nghiem cua ham so trong khoang ( -2.000000 ; -1.000000 ) la: -1.817070 +- 0.000008 Cach 1: Giai ham y = exp(x^3) - 5*x^3 - 30 bang phuong phap chia doi cho khoang nghiem ( a ; b )=( 2 ; 1 ) buoc a Nghiem x b f(a) f(x) Sai so 1 2.00000 1.58596 1.17191 2910.95799 4.06013 0.41404 2 1.58596 1.37893 1.17191 4.06013 -29.34688 0.20702 3 1.58596 1.48245 1.37893 4.06013 -20.29489 0.10351 4 1.58596 1.53420 1.48245 4.06013 -11.04690 0.05176 5 1.58596 1.56008 1.53420 4.06013 -4.41817 0.02588 6 1.58596 1.57302 1.56008 4.06013 -0.44029 0.01294 7 1.58596 1.57949 1.57302 4.06013 1.74039 0.00647 8 1.57949 1.57625 1.57302 1.74039 0.63322 0.00323 9 1.57625 1.57463 1.57302 0.63322 0.09232 0.00162 10 1.57463 1.57383 1.57302 0.09232 -0.17501 0.00081 11 1.57463 1.57423 1.57383 0.09232 -0.04160 0.00040 12 1.57463 1.57443 1.57423 0.09232 0.02530 0.00020 13 1.57443 1.57433 1.57423 0.02530 -0.00817 0.00010 14 1.57443 1.57438 1.57433 0.02530 0.00856 0.00005 15 1.57438 1.57436 1.57433 0.00856 0.00019 0.00003 16 1.57436 1.57434 1.57433 0.00019 -0.00399 0.00001 17 1.57436 1.57435 1.57434 0.00019 -0.00190 0.00001 Nghiem cua ham so trong khoang ( 2.000000 ; 1.171912 ) la: 1.57435 +- 0.00001 Cach 2: Giai ham y = exp(x^3) - 5*x^3 - 30 bang phuong phap tiep tuyen trong khoang nghiem ( 2 ; 1 ) Chon nghiem ban dau x0 = 2.00000 buoc Nghiem x f(x) f'(x) Sai so 1 2.00000 2910.95799 35711.49584 0.08151 1 1.91849 1100.49845 12817.33964 0.08586 2 1.83263 410.25192 4695.47867 0.08737 3 1.74525 146.96778 1814.27432 0.08101 4 1.66425 47.38722 792.98371 0.05976 5 1.60449 11.56131 441.87520 0.02616 6 1.57833 1.33925 343.76029 0.00390 7 1.57443 0.02461 331.20906 0.00007 8 1.57435610 0.00000872 330.97436899 0.00000003 Nghiem cua ham so trong khoang ( 2.000000 ; 1.171912 ) la: 1.57435607 +- 0.00000003 Cach 3: Giai ham y = exp(x^3) - 5*x^3 - 30 bang phuong phap day cung trong khoang nghiem ( a; b ) = ( 2 ; 1 ) buoc a x b f(a) f(x) f(b) Sai so 1 2.00000 1.18121 1.17191 2910.95799 -33.04341 -33.04719 0.81879 2 2.00000 1.19040 1.18121 2910.95799 -33.03181 -33.04341 0.00919 3 2.00000 1.19948 1.19040 2910.95799 -33.01201 -33.03181 0.00908 4 2.00000 1.20846 1.19948 2910.95799 -32.98360 -33.01201 0.00898 5 2.00000 1.21733 1.20846 2910.95799 -32.94617 -32.98360 0.00887 6 2.00000 1.22609 1.21733 2910.95799 -32.89934 -32.94617 0.00876 7 2.00000 1.23473 1.22609 2910.95799 -32.84269 -32.89934 0.00865 8 2.00000 1.24327 1.23473 2910.95799 -32.77583 -32.84269 0.00854 9 2.00000 1.25170 1.24327 2910.95799 -32.69837 -32.77583 0.00843 10 2.00000 1.26001 1.25170 2910.95799 -32.60993 -32.69837 0.00831 11 2.00000 1.26821 1.26001 2910.95799 -32.51013 -32.60993 0.00820 12 2.00000 1.27629 1.26821 2910.95799 -32.39862 -32.51013 0.00808 13 2.00000 1.28426 1.27629 2910.95799 -32.27503 -32.39862 0.00797 14 2.00000 1.29211 1.28426 2910.95799 -32.13905 -32.27503 0.00785 15 2.00000 1.29984 1.29211 2910.95799 -31.99035 -32.13905 0.00773 16 2.00000 1.30745 1.29984 2910.95799 -31.82864 -31.99035 0.00761 17 2.00000 1.31494 1.30745 2910.95799 -31.65367 -31.82864 0.00749 18 2.00000 1.32231 1.31494 2910.95799 -31.46518 -31.65367 0.00737 19 2.00000 1.32955 1.32231 2910.95799 -31.26296 -31.46518 0.00725 20 2.00000 1.33668 1.32955 2910.95799 -31.04684 -31.26296 0.00712 Ham hooi tu qua cham, 20 buoc giai chua ket thuc, dung phuwowng phaps khac Cau 2: tim nghiem nho nhat cua ham so y=f(x)=0 voi sai so 1e-5 y=log(x) - 7*x + x.^2 -5 ; Loi giai: Ham so log(x) - 7*x + x^2 - 5 khong xac dinh trong vung [ -Inf, 0 ]. Ham co dao ham: y' = 2*x + 1/x - 7. Dao ham co nghiem tai cac diem: 0.14922 3.35078. Bang Khao sat ham so log(x) - 7*x + x^2 - 5. x -Inf 0.00000 0.14922 1.75000 3.35078 7.00000 8.00000 Inf y' + 0 - 0 + + + y -Inf -7.9246069435146911 -13.6278842120645773 -16.0185402370452543 -3.0540898509446848 5.0794415416798344 Inf Ham co nghiem trong cac khoang: ( 8.00000 7.00000 ) Cach 1: Giai ham y = log(x) - 7*x + x^2 - 5 bang phuong phap chia doi cho khoang nghiem ( a ; b )=( 8 ; 7 ) buoc a Nghiem x b f(a) f(x) Sai so 1 8.00000 7.50000 7.00000 5.07944 0.76490 0.50000 2 7.50000 7.25000 7.00000 0.76490 -1.20650 0.25000 3 7.50000 7.37500 7.25000 0.76490 -0.23628 0.12500 4 7.50000 7.43750 7.37500 0.76490 0.26044 0.06250 5 7.43750 7.40625 7.37500 0.26044 0.01111 0.03125 6 7.40625 7.39062 7.37500 0.01111 -0.11282 0.01562 7 7.40625 7.39844 7.39062 0.01111 -0.05092 0.00781 8 7.40625 7.40234 7.39844 0.01111 -0.01992 0.00391 9 7.40625 7.40430 7.40234 0.01111 -0.00441 0.00195 10 7.40625 7.40527 7.40430 0.01111 0.00335 0.00098 11 7.40527 7.40479 7.40430 0.00335 -0.00053 0.00049 12 7.40527 7.40503 7.40479 0.00335 0.00141 0.00024 13 7.40503 7.40491 7.40479 0.00141 0.00044 0.00012 14 7.40491 7.40485 7.40479 0.00044 -0.00004 0.00006 15 7.40491 7.40488 7.40485 0.00044 0.00020 0.00003 16 7.40488 7.40486 7.40485 0.00020 0.00008 0.00002 17 7.40486 7.40485 7.40485 0.00008 0.00002 0.00001 Nghiem cua ham so trong khoang ( 8.000000 ; 7.000000 ) la: 7.40485 +- 0.00001 Cach 2: Giai ham y = log(x) - 7*x + x^2 - 5 bang phuong phap tiep tuyen trong khoang nghiem ( 8 ; 7 ) Chon nghiem ban dau x0 = 8.00000 buoc Nghiem x f(x) f'(x) Sai so 1 8.00000 5.07944 9.12500 0.55665 1 7.44335 0.30732 8.02105 0.03831 2 7.40503 0.00145 7.94511 0.00018 3 7.404851425 0.000000033 7.944749448 0.000000004 Nghiem cua ham so trong khoang ( 8.000000 ; 7.000000 ) la: 7.404851421 +- 0.000000004 Cach 3: Giai ham y = log(x) - 7*x + x^2 - 5 bang phuong phap day cung trong khoang nghiem ( a; b ) = ( 8 ; 7 ) buoc a x b f(a) f(x) f(b) Sai so 1 8.00000 7.37549 7.00000 5.07944 -0.23239 -3.05409 0.62451 2 8.00000 7.40282 7.37549 5.07944 -0.01617 -0.23239 0.02732 3 8.00000 7.40471 7.40282 5.07944 -0.00112 -0.01617 0.00190 4 8.00000 7.40484 7.40471 5.07944 -0.00008 -0.00112 0.00013 5 8.000000 7.404851 7.404842 5.079442 -0.000005 -0.000077 0.000009 Nghiem cua ham so trong khoang ( 8.000000 ; 7.000000 ) la: 7.404851 +- 0.000009