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How do you find the limit of # (3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1)) # as x approaches infinity?

1 Answer

Sep 28, 2016

#3/4#

Explanation:

# (3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1))=x^4/x^4(3+4/x^4)/((1-7/x^2)(4-1/x^2))# so

#lim_(x->oo) (3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1)) = lim_(x->oo)(3+4/x^4)/((1-7/x^2)(4-1/x^2)) = 3/4#

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