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1. Maclaurin Expansion of sin(x): The Maclaurin series (Taylor series at $x = 0$) for $f(x) = sin(x)$ is given by: $f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} x^n$

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📐 数学难度 3 — 🟢 Basictaylor_series👁 14 浏览次数⏱ 1 min read

Solve: Find the Taylor series expansion of f(x) = sin…

📝 Problem

Find the Taylor series expansion of f(x) = sin(x) centered at x = 0.

✨详细解答

1. Maclaurin Expansion of sin(x): The Maclaurin series (Taylor series at f(x) = sin(x)$ is given by:

2. General Form: Series representation using Sigma (Σ) notation.

3. First Few Terms: Writing out the first few terms of the expansion:

🔒 3 步剩余

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1. Maclaurin Expansion of sin(x): The Maclaurin series (Taylor series at f(x) = sin(x)$ is given by:

2. General Form: Series representation using Sigma (Σ) notation.

3. First Few Terms: Writing out the first few terms of the expansion:

🔒 3 步剩余

📐 Lv.7

Solve Expand f(x) = sin(x) as a Taylor series about x = 0, keeping the first 5 term... — Step-by-Step Solution by AhaStep