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

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

📝 Problem

Expand f(x) = sin(x) as a Taylor series about x = 0, keeping the first 5 terms. Estimate the value at x = 0.1 and the error.

✨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.4

Giải bài tập Khai triển hàm f(x) = cos(x) thành chuỗi Taylor tại x = 0, giữ 3 số hạng đầu.... — Lời giải chi tiết AhaStep