lim x->infinity (2x^4-3x^2+2x-1)/(x^3-2x^2+2)?

This limit= infinity
take x^4 as a common factor from nominator and denominator, then cancel them. After that substitute directly to get infinity.

that limit would equal infinity. you can tell because the numerator has a higher power of x than the denominator.

if you want to see it better, divide the top and bottom by x^4 and you get the fraction going to 2/0

The exponent of the numerator exceeds that of the denominator, so as x goes to infinity, the expression goes to infinity.
You can prove it by using L'Hopital's Rule should you wish.
lim x-> inf (2x^4-3x^2+2x-1) / (x^3-2x^2+2)
lim x->inf (8x^3 -6x^2+2) / (3x^2-4x)
lim x-> inf (24x^2-12x) / (6x-4)
lim x-> inf (48x-12) / 6
= infinity

divide top and bottom by x^3 ?

limit does not exist ?