## anonymous 3 years ago how do you find the limit of this (attached) algebraically?

1. anonymous

attached??

2. anonymous

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

3. anonymous

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. anonymous

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. anonymous

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

6. anonymous

then it would be 0

7. anonymous

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