Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Limits
Trigonometric Functions
Exponential Functions
Formulas
lim_{x → 0} (cos 2x)^{cot x / sin x} = e^{-2}
cot(x) = cos(x) / sin(x)
sin(x) ≈ x (small-angle approximation)
ln y = lim_{x → 0} (1/x^2) ln(cos(2x))
Theorems
L'Hopital's Rule
Small-angle approximation
Suitable Grade Level
Undergraduate Calculus