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# Find the limit or show that it does not exist. $\displaystyle \lim_{x \to -\infty} \frac{1 + x^6}{x^4 + 1}$

## $\infty$

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##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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### Video Transcript

This is problem number thirty four of the Stewart character. The Safe Edition Section two point six. Find the limit or show, but it does not exist. The Ltd's expertise. Negative infinity. I want those extra sixth over X to the force of plus one s o. One thing Khun do is we can make a choice defending the numerator and the denominator by exit the fourth and in this case, choosing anything greater than except forthe, such as Exit six. Ah, well, not benefit us since it will make the dominator a purse era. So the choice effects of the fourth should work well. Numerator becomes one of Rex to the fourth plys X squared. Since that is extra sixty minute makes in the fourth continuing to do any extra forth and the new denominator yet one plus one of Rex of the Force Ah, as we know a pro as we approach negative infinity, Each of these terms won a race for the fourth vanishes The approach Ciro and what were left over with is X squared over one. And as we approach negative infinity X squared approaches positive infinity. So this functioned averages does not the limit is that exists as thie limited approaching positive infinity as experts native

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