Question

use the properties of limits to help decide whether the limit exists. if limit exist find it's value...

lim -4x^6+ 3x^3 + 6x /
x> infinity 3x^2 - 7x +2

Answer 1

I assumed
\[\huge \lim_{x \rightarrow \infty} \frac{-4x^6+ 3x^3 + 6x}{ 3x^2 - 7x +2}\]

Answer 2

Yes

Answer 3

ok, we have the highest degree at the numerator, so when x approaches infiinity (means x is getting larger values), the whole fraction gets very large because the power is higher at numerator.

and the highest power is negative, so you will get
\[- \infty\]

Answer 4

That limit is not exist

Answer 5

Awesome! Thank you so much!