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What is the limit of #(-5x^3) /( 3x^2-1) # as x approaches infinity?

Answer 1

Ezra Adams

#= - oo #

#lim_{x to oo} (-5x^3) /( 3x^2-1) #

#=lim_{x to oo} -x * (5) /( 3-1/x^2) #

#= lim_{x to oo} -x * lim_{x to oo} (5) /( 3-1/x^2) # (as both these limits exist)

#= - oo * (5) / 3 #

#= - oo #

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Answer 2

Aurora Alvarado

The limit of (-5x^3) /( 3x^2-1) as x approaches infinity is -5/3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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