## Math Problem Statement

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Continuity

Piecewise Functions

Limits

### Formulas

Left-hand limit: \( \lim_{x \to 0^-} f(x) \)

Right-hand limit: \( \lim_{x \to 0^+} f(x) \)

Continuity condition: \( \lim_{x \to 0^-} f(x) = f(0) = \lim_{x \to 0^+} f(x) \)

### Theorems

Continuity of piecewise functions at a point

Limit properties of trigonometric functions

### Suitable Grade Level

Undergraduate Calculus or Advanced High School Calculus

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