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

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Answer 1 · 2016-08-11T17:31:58

$= - oo$

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

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

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

$= - oo * (5) / 3$

$= - oo$

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