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Pilih semua barisan yang konvergen.

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Pilih semua deret yang konvergen.

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Jari-jari kekonvergenan Deret Taylor dari $f(x)$ di sekitar \$a=\\var{b}\$ dengan \$ f^{(n)}(\\var{b})=\\dfrac{(-e)^nn!}{\\var{r}^nn^n}\$ untuk \$n=0,1,2,\\cdots\$ adalah $\\ldots$.

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Misalkan \$ f(x)=\\cos(x^3) \$ dan nilai dari \$f^{(12)}(0)= a\$.

Maka \$ \\dfrac{a}{6!}=\\ldots \$.

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Fungsi \$ f(x)=\\dfrac{1}{1+x-x^2} \$ mempunyai Deret Maclaurin \$ \\displaystyle\\sum_{n=0}^\\infty (-1)^nf_nx^n\$ (pada daerah kekonvergenannya) dengan \$ f_n \$ menyatakan suku ke-$n$ dari barisan Fibonacci, yakni $f_1=1$, $f_2=1$, dan $f_n=f_{n-1}+f_{n-2}$ untuk \$ n\\geq 3\$.

Polinom Taylor orde $6$ dari $f(x)$ di sekitar \$x=\\dfrac{1}{2}\$ adalah

\$f(x)\\approx\$ [[0]] $+$ [[1]] \$\\left( x-\\dfrac{1}{2} \\right)^2\$ $+$ [[2]] \$\\left( x-\\dfrac{1}{2} \\right)^4\$ $+$ [[3]] \$\\left( x-\\dfrac{1}{2} \\right)^6\$.

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Koefisien suku \$ \\left( x-\\dfrac{1}{2} \\right)^{40} \$ dari uraian Deret Taylor \$ f(x) \$ di sekitar \$ x=\\dfrac{1}{2} \$ berbentuk \$ \\dfrac{a^{10}}{b^{10}} \$ dengan \$ a\$ dan \$ b\$ bilangan bulat. Maka \$ a+b =\\ldots\$.

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Nilai dari \$ f^{(40)}\\left(\\dfrac{1}{2}\\right) = n!\\cdot \\dfrac{a^{10}}{b^{10}}\$ dengan \$a\$, \$b\$, dan \$n\$ bilangan bulat. Maka \$a+b+n=\\ldots\$.

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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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