# Thread: Evaluating limits at infinity

1. ## Evaluating limits at infinity

http://i754.photobucket.com/albums/x...at111757AM.png

I need help with the 2nd part of the question, evaluating the limit at neg infinity.

I'm dividing the numerator by the highest power in the denominator (dividing everything by x^3 and x^6 under the radical) and I'm coming up with...

Lim x-> -oo f(x) = 3+6(1/x^3) / [3 + sqrt((36 + 4(1/x^6))]

1/x^3 approaches 0 as x approaches neg infinity and 1/x^6 approaches zero as x approaches infinity. leaving me with...

3 / [(3+sqrt(36)] =3 / (3+3) = 1/3.

The correct answer is -1. Where did I go wrong?

2. ## Re: Evaluating limits at infinity

Originally Posted by Johnny Walker Black
The correct answer is -1. Where did I go wrong?
If $\displaystyle x<0$ then, $\displaystyle x^3<0$ so,

$\displaystyle \frac{\sqrt{36x^6+4}}{x^3}=-\frac{\sqrt{36x^6+4}}{|x|^3}=-\sqrt{\frac{36x^6}{|x|^6}+\frac{4}{|x|^6}}=-\sqrt{36+\frac{4}{|x|^6}}\to -6$ as $\displaystyle x\to -\infty$

Hence, the asked limit is $\displaystyle -1$ .