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## Homework Statement

Evaluate: ##\lim_{x \rightarrow -\infty} {\frac{3x^3+2}{\sqrt{x^4-2}}}##

## Homework Equations

## The Attempt at a Solution

For limits involving fractions, it's a good idea to divide the numerator and the denominator by the highest degree x in the fraction. In doing this, we can separate the constituent pieces and evaluate them individually as the limit goes to ##a##.

Now in this problem, with exponents under radicals, I am having a small hiccup.

In the numerator, we have ##x^3##, and in the denominator we have ##x^4## under a radical which can be seen as ##x^\frac{4}{2}## which is the same as ##x^2##.

So with this reasoning, I see ##x^3## as the higher degree and divide the numerator and denominator by ##x^3## and go on to break it apart.

However, in doing this, I get an indeterminate result ##\frac{0}{0}## which I do not want. Next I tried to divide by ##x^2## or ##\sqrt{x^4}##

This gives me a better solution which tells me the limit goes to -∞.

Now my question is, why did dividing by the lesser degree provide the limit, but the higher degree did not? Or

*is*the ##x^4## the higher degree even though it's under a radical?

Thank you for reading!