// Numbas version: exam_results_page_options {"name": "Set Soal Matematika Bisnis II - Bab 5 - 10", "metadata": {"description": "", "licence": "None specified"}, "duration": 3600, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "PG + Isian", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "questions": [{"name": "Matbis 2 - UAS - No 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Pilihlah semua persamaan diferensial yang konvergen ke solusi steady state-nya.

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Pilihlah semua selang di mana fungsi \$ f(x)=e^x-x^3+x-4\$ mempunyai akar.

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Pilihlah semua pernyataan yang benar berdasarkan beda terbagi Newton dari tabel fungsi berikut.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\$x\$	\$ f(x) \$
$1$	$4$
$2$	$6$
$3$	$9$
$4$	$14$

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Misalkan polinom interpolasi Lagrange orde $2$ dari suatu fungsi adalah $f(x)$ dengan $f(\\var{a})=\\var{a1}$, $f(\\var{b})=\\var{b1}$, dan $f(\\var{c})=\\var{c1}$.

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Maka $f(\\var{x})=\\ldots$.

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Hasil dua iterasi pertama metode Newton-Raphson untuk menentukan hampiran akar dari \$ f(x)=x^3-2x+5\$ dengan \$x_0=1\$ adalah \$\\ldots\$.

\$x_1=\$[[0]] dan \$x_2=\$[[1]].

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Solusi dari persamaan diferensial \$ y''-4y'+4y=t^2+3\$ adalah \$ y=C_1e^{2t}+C_2 te^{2t}+f(t)\$.

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Maka \$ f(\\var{a})=\\ldots\$.

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Suatu perusahaan minyak menjual dua buah jenis produk minyak: minyak mentah yang belum diolah dan minyak mentah yang sudah diolah menjadi BBM. Misalkan harga BBM adalah \$ x_t \$ dan harga minyak yang belum diolah adalah \$ y_t \$. Harga BBM pekan ini bergantung pada harga BBM pekan sebelumnya dan harga minyak mentah pekan sebelumnya, yakni \$ x_{t+1}=\\alpha x_t+\\beta y_t \$.

Pemompaan minyak mentah ke permukaan membutuhkan BBM, sehingga harga minyak bumi bergantung pada harga BBM. Harga minyak mentah juga bergantung pada faktor luar \$ f(t) \$, sehingga \$ y_{t+1} =\\delta x_t +f(t)\$.

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Jika \$ \\alpha=\\dfrac{1}{\\var{a}}, \\beta= {\\var{b}} \$, dan \$ \\delta=\\dfrac{1}{\\var{c}}\$. Maka persamaan beda untuk harga BBM adalah

\$ x_{t+2}=\$ [[0]]\$x_{t+1}+\$ [[1]]\$x_t+\$ [[2]]\$f(t)\$.

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Solusi homogen persamaan beda tersebut adalah \$y_t=C_1r_1^t+C_2r_2^t\$.

Jika \$r_1>r_2\$, maka \$r_1=\$ [[0]] dan \$ r_2=\$ [[1]].

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Jika \$ f(t)=\\var{d}\$, maka persamaan beda tersebut akan konvergen ke [[0]].

Waktunya 5 menit lagi ya.

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Selamat datang!

Silakan gunakan set soal ini dengan bijak. Kalian bisa mencoba set soal ini terus-menerus.

Set soal ini dapat digunakan oleh siapapun secara gratis.

Petunjuk pengerjaan soal:

Jawaban dapat dituliskan dalam bentuk desimal maupun pecahan.
Jika jawaban dituliskan dalam bentuk desimal, pisahkan dengan tanda titik dan bulatkan hingga dua angka di belakang titik. Contoh: ketik 0.67 untuk menjawab \$\\frac{2}{3}\$.
Jika jawaban dituliskan dalam bentuk pecahan, pisahkan pembilang dan penyebut dengan garis miring dan jawab dengan pecahan paling sederhana. Contoh: ketik 2/3 untuk menjawab \$\\frac{2}{3}\$.

Jika ada kunci jawaban yang salah, kalian dapat memberitahu kami di Instagram @meongmeongproject atau OA Line @eog7710d.

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