Math Problem Statement

Evaluate the limit lim x→0 (1 - cos(x)) / x².

Solution

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Math Problem Analysis

Mathematical Concepts

Limits
Trigonometry
L'Hôpital's Rule

Formulas

cos(x) ≈ 1 - x²/2 for small x (trigonometric approximation)
L'Hôpital's Rule: lim x→c f(x)/g(x) = lim x→c f'(x)/g'(x) when indeterminate

Theorems

L'Hôpital's Rule
Taylor Series Expansion

Suitable Grade Level

Undergraduate Calculus