how do you find the limit of this (attached) algebraically?

Question

anonymous · Answer

attached??

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

then it would be 0

anonymous · Answer

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