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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))

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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