1. ## Limit of Infinity

limit -x^5 + x - 1 as x goes to infinity

-(infinity)^5 + infinity - 1 = -infinity + infinity (is it now positive or negative infinity?)

2. ## Re: Limit of Infinity

Hey joshuaa.

Have you studied limits?

3. ## Re: Limit of Infinity

yes but i am confused cuz the dr. says infinity - infinity is indeterminate. so will i add them or i cannot?

4. ## Re: Limit of Infinity

Originally Posted by joshuaa
limit -x^5 + x - 1 as x goes to infinity

-(infinity)^5 + infinity - 1 = -infinity + infinity (is it now positive or negative infinity?)
You can't add infinities...infinity is not a number. But we can still do a comparison. Which is bigger for large numbers (not infinite ones), $x^5$ or x?

-Dan

5. ## Re: Limit of Infinity

Originally Posted by topsquark
You can't add infinities...infinity is not a number. But we can still do a comparison. Which is bigger for large numbers (not infinite ones), $x^5$ or x?
Better is to write $-x^5+x = x(1-x^4) \to \infty \cdot (-\infty) = -\infty$
Or $-x^5+x > -x^5$ (where $x > 0$).

6. ## Re: Limit of Infinity

From precalculus, recall the end behavior of an odd-degree polynomial with a negative leading coefficient.

thanks guys