## ksandoval 2 years ago how do you find the limit of this (attached) algebraically?

1. robinfr93

attached??

2. ksandoval

$\lim_{x \rightarrow \pm \infty} \frac{ x^4 + x^3 }{ 12x^3 + 128 }$

3. satellite73

numerator is larger than the denominator, so no limit or you could say $$\infty$$ as $$x\to \infty$$ and $$-\infty$$ as $$x\to -\infty$$

4. jamesumner93

you can see that the top gets larger faster than the bottom so it is either going to be positive infinity or negative infinity, depending on if your taking the limit as x approaches infinity or negative infinity respectively

5. ksandoval

oh. thats all you do? okay! so what if the denominator was larger?

6. jamesumner93

then it would be 0

7. jamesumner93

because it would be like 1/2 , 1/4. 1/8, 1/16. 1/32, 1/64 (closer and closer to 0)