## Math Problem Statement

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Limits

Series

Exponential Functions

Trigonometric Functions

### Formulas

Limit: \( \lim_{x \to 0} f(x) \)

Series: \( \sum_{n=1}^{\infty} a_n \)

Exponential Function: \( e^x \)

Sine Function: \( \sin(x) \)

Taylor Series Expansion: \( \sin(x) \approx x \text{ for small } x \)

### Theorems

Taylor Series Expansion

Properties of Limits

Convergence of Series

### Suitable Grade Level

Undergraduate

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