1. Gunakan pendekatan interpolasi Newton/Lagrange untuk memodelkan himpunan (x,y) berikut (Seluruh titik harus dilewati secara sempurna)!(0,4)(2,6)(4,8)(6,6)(9,10)(11,8)(12,7)(15,10)(17,12)(19,13)2. Evaluasilah integral f(x) = 9 + 3*sin(x) dari x = 0 hingga x = pi/2, secara: (a) analytik (b) Aplikasi Trapezoidal aplikasi tunggal (c) Simpson aplikasi tunggal! Carilah error di setiap pendekatan numerik!3. Carilah nilai y(x=0) hingga y(x=2) dengan step size h = 0.25 dari suatu sistem yang dimodelkan. Diketahui y(0) = 1:y' = (1+3*x)*ySelesaikanlah secara analitik, Euler, dan juga Heun!Catatan: Anda bisa menggunakan pendekatan pemisahan variabel untuk memecahkan sistem tersebut secara analitik4. Diketahui suatu persamaan differential cauchy: (x^2) y'' - 5 x y' + 9 y = 0 memiliki solusi umum y = (c1 + c2*ln(x))*(x^3)Carilah solusi dari persamaan differential tersebut secara numerik sehingga error yang didapat saat y(x=2) adalah di bawah 0.1%! Catatan: Anda diperbolehkan menentukan sendiri step size h dan syarat nilai awal yang anda perlukan (selain nilai x = 2)!5. Di bawah ini adalah data pembacaan suatu sensor yang diterima setiap bulannya. Prediksikanlah pembacaan sensor tersebut pada pertengahan bulan Januari tahun berikutnya memanfaatkan konsep linear regresi sehingga didapat koefisien korelasi di atas 0.99:Bulan:Januari 70Februari 73Maret 60April 58Mei 52Juni 43Juli 33Agustus 27September 29Oktober 39November 50Desember 626. Di bawah ini adalah data pasangan (x,y) di suatu kurva. Dengan menggunakan konsep interpolasi, prediksikanlah nilai y saat x = 47.75 sehingga error yang didapat adalah di bawah 0.1%! Berapa orde polynomial minimal yang diperlukan untuk memenuhi kriteria error tersebut? Berikan alasan anda kenapa orde tersebut cukup!Sebagai rujukan, diketahui bahwa nilai y saat x=47.75 yang sebenarnya adalah 18.45984192(0 , 0 )(0.5 , 0.17040969 )(1 , 0.239712769 )(1.5 , 0.185552969 )(2 , 0 )(2.5 , -0.309254949)(3 , -0.719138308 )(3.5 , -1.19286783 )(4 , -1.68294197 )(4.5 , -2.135215394)(5 , -2.493737467 )(5.5 , -2.705961354)(6 , -2.72789228 )(6.5 , -2.52873789 )(7 , -2.094652504 )(7.5 , -1.43122872 )(8 , -0.564480032 )(8.5 , 0.459829322 )(9 , 1.578524525 )(9.5 , 2.714916264 )(10 , 3.784012477 )(10.5 , 4.698694131 )(11 , 5.376415647 )(11.5 , 5.745933537 )(12 , 5.753545648 )(12.5 , 5.368340584 )(13 , 4.586012116 )(13.5 , 3.430883773 )(14 , 1.955908487 )(14.5 , 0.24054932 )(15 , -1.613399911 )(15.5 , -3.487841572)(16 , -5.25589279 )(16.5 , -6.790417252)(17 , -7.972999803 )(17.5 , -8.702739317)(18 , -8.90422422 )(18.5 , -8.534088945)(19 , -7.58562757 )(19.5 , -6.091058549)(20 , -4.121184852 )(20.5 , -1.782367225)(21 , 0.789086765 )(21.5 , 3.434831331 )(22 , 5.98423222 )(22.5 , 8.265357342 )(23 , 10.11650124 )(23.5 , 11.39747495 )(24 , 11.99988248 )(24.5 , 11.85564797 )(25 , 10.94315218 )(25.5 , 9.290478442 )(26 , 6.975447934 )(26.5 , 4.122331453 )(27 , 0.895345614 )(27.5 , -2.510738101)(28 , -5.882338516 )(28.5 , -9.000456575)(29 , -11.65487418 )(29.5 , -13.65824103)(30 , -14.85911034 )(30.5 , -15.15302679)(31 , -14.49087336 )(31.5 , -12.88384277)(32 , -10.40460544 )(32.5 , -7.184485239)(33 , -3.406713452 )(33.5 , 0.703907908 )(34 , 4.894356383 )(34.5 , 8.898961858 )(35 , 12.45624349 )(35.5 , 15.32594414 )(36 , 17.30515485 )(36.5 , 18.2424531 )(37 , 18.0490811 )(37.5 , 16.7063595 )(38 , 14.26875769 )(38.5 , 10.86231115 )(39 , 6.67837206 )(39.5 , 1.962983051 )(40 , -2.997544193 )(40.5 , -7.894003377)(41 , -12.41356733 )(41.5 , -16.25975968)(42 , -19.17185027 )(42.5 , -20.94240862)(43 , -21.43184058 )(43.5 , -20.57890232)(44 , -18.40642405 )(44.5 , -15.02176829)(45 , -10.61187757 )(45.5 , -5.433112322)(46 , 0.203580114 )(46.5 , 5.951312057 )(47 , 11.44860104 )(47.5 , 16.34210098 )(48 , 20.3092897 )(48.5 , 23.07965765 )(49 , 24.45300969 )(49.5 , 24.31364982 )(50 , 22.63945905 )(50.5 , 19.50518459 )(51 , 15.07961701 )(51.5 , 9.616717436 )(52 , 3.441145503 )(52.5 , -3.070993941)(53 , -9.515046382 )(53.5 , -15.48295225)(54 , -20.58907816 )(54.5 , -24.49510012)(55 , -26.93233519 )(55.5 , -27.72005261)(56 , -26.778526 )(56.5 , -24.13590218)(57 , -19.9283409 )(57.5 , -14.39329897)(58 , -7.856267861 )(58.5 , -0.711695816)(59 , 6.600791386 )(59.5 , 13.6234389 )(60 , 19.90901653 )(60.5 , 25.04928413 )(61 , 28.70145795 )(61.5 , 30.61096489 )(62 , 30.62898035 )(62.5 , 28.72355294 )(63 , 24.98350804 )(63.5 , 19.61476819 )(64 , 12.92920465 )(64.5 , 5.326610349 )(65 , -2.72916981 )(65.5 , -10.73852846)(66 , -18.19708048 )(66.5 , -24.62742125)(67 , -29.60965919 )(67.5 , -32.80877128)(68 , -33.99700324 )(68.5 , -33.06982385)(69 , -30.05433001 )(69.5 , -25.10946153)(70 , -18.51789401 )(70.5 , -10.67000372)(71 , -2.040805473 )(71.5 , 6.83877758 )(72 , 15.4145761 )(72.5 , 23.14375946 )(73 , 29.52918497 )(73.5 , 34.15133868 )(74 , 36.69581758 )(74.5 , 36.97455764 )(75 , 34.93938329 )(75.5 , 30.68692057 )(76 , 24.45444907 )(76.5 , 16.60683513 )(77 , 7.615253786 )(77.5 , -1.97106511 )(78 , -11.55837457 )(78.5 , -20.54518478)(79 , -28.35999641 )(79.5 , -34.49762598)(80 , -38.55181545 )(80.5 , -40.24202402)(81 , -39.43264096 )(81.5 , -36.14331494)(82 , -30.54963958 )(82.5 , -22.97403404)(83 , -13.86727384 )(83.5 , -3.78172219 )(84 , 6.66215209 )(84.5 , 16.81394184 )(85 , 26.0338065 )(85.5 , 33.73279217 )(86 , 39.41042656 )(86.5 , 42.68719048 )(87 , 43.32976289 )(87.5 , 41.26736726 )(88 , 36.59808868 )(88.5 , 29.58464958 )(89 , 20.63979046 )(89.5 , 10.30205762 )(90 , -0.79658663 )(90.5 , -11.96938558)(91 , -22.51728195 )(91.5 , -31.77265465)(92 , -39.14156213 )(92.5 , -44.14182022)(93 , -46.43447557 )(93.5 , -45.84662481)(94 , -42.38405234 )(94.5 , -36.23278351)(95 , -27.74933776 )(95.5 , -17.44017455)(96 , -5.931509892 )(96.5 , 6.068701185 )(97 , 17.81430943 )(97.5 , 28.56736547 )(98 , 37.6444784 )(98.5 , 44.46022713 )(99 , 48.56486771 )(99.5 , 49.67391125 )(100 , 47.68763264 )Di bawah ini adalah pasangan (x,y) dari suatu kurva. Carilah integral fungsi tersebut dari x = 0 hingga x = 7. Hitunglah hingga ketelitian 10 angka penting! Menurut anda, apakah dengan tools (excel/Matlab/C) yang anda gunakan, mungkinkah mendapatkan ketelitian tersebut? Berikan alasannya(0,0)(0.1,0.009999833 )(0.2,0.039989334 )(0.3,0.089878549 )(0.4,0.159318207 )(0.5,0.247403959 )(0.6,0.352274233 )(0.7,0.470625888 )(0.8,0.597195441 )(0.9,0.724287174 )(1 ,0.841470985 )(1.1,0.935616002 )(1.2,0.991458348 )(1.3,0.992903651 )(1.4,0.925211521 )(1.5,0.778073197 )(1.6,0.549355436 )(1.7,0.248946787 )(1.8,-0.098248594)(1.9,-0.451465752)(2 ,-0.756802495)(2.1,-0.954627772)(2.2,-0.991868757)(2.3,-0.83776948 )(2.4,-0.499641883)(2.5,-0.033179217)(2.6,0.458951486 )(2.7,0.845133412 )(2.8,0.999902259 )(2.9,0.849363379 )(3 ,0.412118485 )(3.1,-0.184164779)(3.2,-0.72787787 )(3.3,-0.994432209)(3.4,-0.844895944)(3.5,-0.311119355)(3.6,0.383542755 )(3.7,0.90167577 )(3.8,0.95449543 )(3.9,0.477637145 )(4 ,-0.287903317)(4.1,-0.892129365)(4.2,-0.935459141)(4.3,-0.351858587)(4.4,0.488564766 )(4.5,0.985525112 )(4.6,0.73870603 )(4.7,-0.098690514)(4.8,-0.866851156)(4.9,-0.901291364)(5 ,-0.13235175 )(5.1,0.768989408 )(5.2,0.943928493 )(5.3,0.183291742 )(5.4,-0.774336661)(5.5,-0.919153694)(5.6,-0.055897386)(5.7,0.87914899 )(5.8,0.794096248 )(5.9,-0.249806884)(6 ,-0.991778853)(6.1,-0.469842053)(6.2,0.674943522 )(6.3,0.913051492 )(6.4,-0.119012747)(6.5,-0.986987063)(6.6,-0.409856878)(6.7,0.788091792 )(6.8,0.773211435 )(6.9,-0.467190235)(7 ,-0.953752653)