Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Rational Functions
Limits
Discontinuities
Asymptotes
Formulas
$$ f(x) = \frac{x^3 - 3}{2x^2(1 + 2x)} $$
Solving for when the denominator equals zero: $$ 2x^2(1 + 2x) = 0 $$
Horizontal asymptote: $$ \lim_{x \to \infty} f(x) = \frac{1}{2} $$
Theorems
Limit Theorems
Asymptote Properties
Discontinuity of Rational Functions
Suitable Grade Level
Undergraduate Calculus
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