// Numbas version: exam_results_page_options {"name": "LK Minggu Terakhir", "metadata": {"description": "", "licence": "None specified"}, "duration": 4800, "percentPass": "70", "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Domain dan Range Fungsi Dua Peubah", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Arini Soesatyo Putri", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4647/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Himpunan daerah asal dan daerah hasil dari fungsi $f(x,y)=\\sqrt{1-\\frac{x^2}{9}-\\frac{y^2}{4}}$ secara berturut-turut dituliskan sebagai

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Misalkan didefinisikan fungsi $f(x,y)=\\frac{cos(y)sin(x)}{x}$, jika $x\\neq 0$ dan $f(x,y)=cos(y)$ jika $x=0$.

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Himpunan semua titik sehingga fungsi $f(x,y)$ kontinu adalah

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Gambar di bawah ini adalah kurva ketinggian dari suatu fungsi suhu $T=T(x,y)$ di USA.

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Berdasarkan gambar tersebut, nyatakan laju perubahan suhu ke arah timur laut pada titik P (asumsikan $P=P(1240,1000)$) sebagai turunan berarah. Berapakah besarnya laju perubahan tersebut?

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(Catatan: Gunakan . untuk menuliskan koma)

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Seekor semut berada pada permukaan dengan fungsi ketinggian $f(x,y)=-xye^{-x^2-y^2}$. Pada arah vektor satuan mana semut harus bergerak agar menaik secepat mungkin, bila mula-mula titik awal semut adalah $(-1,1)$? Kemudian taksir ketinggian semut setelah bergerak dalam arah tersebut sejauh $1$ satuan di bidang-xy (Gunakan deret Taylor orde 1)

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Ke arah $\\frac{1}{\\sqrt{2}}\\langle a, b \\rangle$, dengan $a =$ [[0]] dan $b = $ [[1]]

\n

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Hampiran $f(x,y)\\approx $

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(Tuliskan dalam bentuk bilangan desimal hingga tiga digit di belakang koma. Jangan lupa, notasi koma menggunakan titik . )

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Turunan berarah dari fungsi $f(x,y)=cos(2x)sin(3y)$ di titik $(\\frac{\\pi}{3},\\frac{\\pi}{4})$ dalam arah $60^{o}$ terhadap sumbu-$x$ positif dapat dinyatakan dalam bentuk $-\\frac{A}{B}\\sqrt{6}$, di mana $A$ dan $B$ adalah bilangan bulat positif dengan $\\frac{A}{B}$ dalam bentuk paling sederhana. Nilai dari $A+B$ adalah

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Persamaan parametrik garis singgung dari kurva hasil perpotongan permukaan $z=x^{2}+y^{2}$ dan bidang $z=2x+4y+20$ di titik $P(4,-2,20)$ memiliki bentuk

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$x=4+at$

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$y=-2+bt$

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$z=20+ct$

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dengan $a,b,c$ merupakan bilangan-bilangan bulat nonnegatif dengan FPB sama dengan 1.

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Nilai dari $a+b+c=$

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Bidang singgung dari permukaan $2x^2+y^3=(z-1)^4$ di titik $(2,2,3)$ dapat dituliskan sebagai $Ax+By-Cz+D=0$, dengan $A,B,C,D$ bilangan bulat taknegatif dan FPB dari $A,B,C,D$ sama dengan 1

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Nilai dari $A-B+C-D$ adalah

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Suatu kotak persegi panjang tanpa tutup dibuat dari kardus berukuran $12 cm^{2}$. Volume maksimum dari kotak tersebut adalah

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Sebuah gelas berisi kopi panas diletakkan pada meja. Bagian dasar gelas berbentuk cakram tutup, dan dinyatakan sebagai himpunan $B=\\left\\{(x,y)|x^{2}+y^{2}\\leq 1\\right\\}$. Bila temperatur pada meja yang menyentuh dasar gelas adalah

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$T(x,y)=3x^2-2y^2+2y$

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Maka nilai maksimum dan minimum dari $T$ pada $B$ adalah

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Nilai minimum:

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Nilai maksimum:

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Diberikan persamaan

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$\\int_{0}^{1}\\int_{4x}^{4} f(x,y)dydx=\\int_{a}^{b}\\int_{c}^{dy}f(x,y)dxdy$

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Nilai dari $ab+c+4d$ adalah

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Nilai dari integral $\\int_{0}^{1}\\int_{\\sqrt{y}}^{1}e^{y/x}dxdy$ adalah ...

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(Tuliskan dalam notasi pecahan a/b)

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Nilai dari integral

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$\\iint_{A} \\frac{x-y}{x^2+y^2}dxdy$

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dengan $A$ adalah daerah di kuadran I, di dalam lingkaran berpusat di $O$ dan berjari-jari 1, serta di luar segitiga yang memiliki titik sudut $(0,0),(0,1)$, dan $(1,0)$ adalah

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Misalkan $D$ adalah daerah yang diberikan oleh persamaan $r=cos(4\\theta)$ seperti di bawah ini:

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Berapakah luas daerah $D$ tersebut?

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(Catatan: jika hasil yang diperoleh memuat konstanta  $\\pi$, maka tuliskan \"pi\". Misalkan hasilnya adalah $\\frac{\\pi}{17}$, maka tuliskan pi/17.)

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Persamaan diferensial $y\"+9y=e^{3x}+x^3$ memiliki solusi umum berbentuk

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$y=C_{1}cos(\\alpha x)+C_{2}sin(\\beta x)+Ce^{3x}+Dx^{3}+Ex$

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Nilai dari $\\alpha\\frac{C}{E}+\\beta D$ adalah

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(Catatan: Tuliskan dalam bentuk pecahan a/b)

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Persamaan diferensial takhomogen berikut

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$y\"+y'-6y+6x^2-2x-8=0$

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dengan

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$y(0)=2$ dan $y'(0)=1$

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diketahui memiliki solusi berbentuk $y(x)=Ae^{Bx}+Ce^{Dx}+Ex^2+Fx+G$.

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Nilai dari $A+B+C+D+E+F+G$ adalah

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Waktu habis

"}, "timedwarning": {"action": "warn", "message": "

5 menit lagi

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