07:42 ? Ims.dut.udn.vn/mc \( + \) 43 Th?i gian còn l?i 0:16:34 Câu h?i 11 Ch?a trá l? ??t ?i?m 1,00 P ??t c? Find the Maclaurin series for \( f(x)=x \cos (4 x) \). Select the correct answer. a. \( \sum_{n=0}^{\infty} \frac{(-1)^{n} 4^{2 n} x^{2 n+1}}{(2 n)!} \) b. \( \sum_{n=0}^{\infty} \frac{(-1)^{n} 4^{n} x^{2 n+1}}{(2 n)!} \) C. \( \sum_{n=0}^{\infty} \frac{(-1)^{n+1} 4^{2 n} x^{2 n-1}}{(2 n)!} \) d. \( \sum_{n=0}^{\infty} \frac{(-1)^{n} 4^{2 n} x^{2 n}}{(2 n)!} \) e. \( \sum_{n=0}^{\infty} \frac{(-1)^{n} 4^{2 n} x^{2 n+1}}{n!} \) Clear my choice Trang tr??c Trang ti?p
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Step 1: Recall the Maclaurin series for \(\cos(x)\), which is: \[ \cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} \] Show more…
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Use the identity $\cos ^{2} x=\frac{1}{2}(1+\cos 2 x)$ to find the Maclaurin series for $f(x)=\cos ^{2} x$.
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