Math Problem Statement
Berechnen Sie die beiden Grenzwerte mit Hilfe der jeweiligen Potenzreihenentwicklungen: (1) lim (x→0) [ (2x − sin(2x)) / (3x³) ], (2) lim (x→0) [ (4 − 4e^(x⁴)) / (5x⁴) ]
Solution
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Math Problem Analysis
Mathematical Concepts
Limits
Series Expansion
Power Series
Formulas
sin(x) ≈ x - x³/3! + x⁵/5! - ... (Maclaurin series for sin(x))
e^x ≈ 1 + x + x²/2! + x³/3! + ... (Maclaurin series for e^x)
Theorems
Maclaurin Series
Limit of Functions
Suitable Grade Level
Undergraduate Mathematics or Advanced High School Calculus
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