Math Problem Statement
lim x -> infinity(sqrt(1 + x ^ 4) - 1 - x ^ 2)/(x ^ 2) =
A)-1
B0
C-2
D 2
Solution
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Math Problem Analysis
Mathematical Concepts
Limits
Asymptotic Expansion
Infinity
Algebraic Manipulation
Formulas
lim x -> infinity (sqrt(1 + x^4) - 1 - x^2)/(x^2)
Asymptotic expansion: sqrt(1 + x^4) ≈ x^2 + (1/2x^2)
Theorems
Limit Theorem
Asymptotic Approximation
Suitable Grade Level
College-Level Calculus
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