Question

lim as x approaches infinity the sq root of 9x^6-x/x^3+1 (answer is not infinity)

Answer 1

what do you know @JAXXDP and i will help

Answer 2

This?
\[\Large \lim_{x \rightarrow \infty} \dfrac{\sqrt{9x^6 - x}}{x^3+1}\]

Answer 3

yes that it

Answer 4

i thought since the coefficient of the numerator was greater than the denominator's coefficient then it would be DNE which is infinity but my teacher told me that is not the answer

Answer 5

sorry for late reply, but knowing that x approaches to infinity, terms other than leading term would become less and less significant, because leading term approaches infinity fastest.

So basically: \[\lim_{x \rightarrow \infty} \dfrac{\sqrt{9x^6 - x}}{x^3 + 1} = \lim_{x \rightarrow \infty} \dfrac{\sqrt{9x^6}}{x^3}\]Which can be simplified to \(\dfrac{3x^3}{x^3} = \boxed{3}\)