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Question
Thank you for your time and assistance. My question is:

Find the limit of the following when x->infinity (x approaches infinity, I believe):

(4x^4+3x^2-4)/((2x-3)(2x+1)(x^2-2))

Answer
If you expand the denominator, the leading term is also 4x^4. As x -> infinity, the lower order terms will be "overwhelmed" by these highest order terms and become negligible. Since the highest order terms in the numerator and denominator are equal, the limit should go to 1.

A more rigorous way to show this is to apply L'Hopital's Rule and take derivatives of the numerator and denominator (separately) until you get an expression that is not indeterminant (infinity/infinity). This means 4 derivatives -> 96/96 = 1.

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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