Question

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

Answer 1

attached??

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

then it would be 0

Answer 7

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