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Nilai dari \$$\\displaystyle\\lim_{x\\to \\infty} \\left(1+\\frac{1}{{a}x+b}\\right)^x=\\sqrt[\\var{a}]{ce}\$$ , dengan $a$, $b$, dan $c$ bilangan real positif dan $e$ merupakan bilangan Euler.

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Nilai dari $a+c$ adalah $\\ldots$.

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Pilihlah seluruh limit yang merupakan bentuk tak tentu.

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Misalkan $f$ merupakan fungsi yang terturunkan di $\\mathbb{R}$. Diketahui $\\displaystyle\\lim_{h\\to 0} \\frac{f(1+\\var{a}h)-f(1-\\var{a}h)}{h}=\\simplify{2*({a}^2+1)*{a}}$.

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Nilai dari $f'(1)=\\ldots$.

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$\\displaystyle\\int_{\\simplify{-{3}/{2*{a}}}}^{\\infty} \\frac{1}{Ax^2+\\simplify{12*{a}}x+10}\\,dx = \\dfrac{\\pi}{\\simplify{4*{a}}}$ dengan $A=\\ldots$.

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Nilai dari $A$ adalah $\\ldots$.

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Diketahui daerah $D=D_1\\cup D_2$ dibatasi oleh garis $x=\\dfrac{\\pi}{2}$, sumbu-$x$, dan $y=f(x)=e^{-\\var{a}x}\\sin(x)$, $D_1$ merupakan semua daerah yang berada dikuadran $I$ dan $D_2$ merupakan semua daerah yang berada pada kuadran $IV$.

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Misalkan $A_1$ merupakan luas daerah $D_1$ dan $D_2$ merupakan luas $A_2$, dan $\\displaystyle A_1-A_2 = Ae^{-B\\pi}$ dengan $AB=\\ldots$.

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Volume benda putar jika $D$ diputar mengelilingi sumbu-$x$ adalah $K\\pi e^{-\\var{a}\\pi}$ dengan $K=\\ldots$.

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Volume benda putar jika $D_1$ diputar mengelilingi sumbu-$y$ adalah $V_1$ dan volume benda putar jika $D_2$ diputar mengelilingi sumbu-$y$ adalah $V_2$. Jika nilai dari $V_1-V_2=\\dfrac{2\\pi e^{-\\var{a}\\pi/2}}{A}(B\\pi+C)$ maka $A+B+C=\\ldots$.

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Waktunya 5 menit lagi ya.

Selamat datang!

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

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Set soal ini dapat digunakan oleh siapapun secara gratis.

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Petunjuk pengerjaan soal:

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• Jawaban dapat dituliskan dalam bentuk desimal maupun pecahan.
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• 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}\$$.
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• 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}\$$.
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Jika ada kunci jawaban yang salah, kalian dapat memberitahu kami di Instagram @meongmeongproject atau OA Line @eog7710d.

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