lim x-> infinity, (3 - 2x^2) / (3x - 1). Why is the answer negative infinity instead of positive infinity if x is approaching positive infinity?

Answer 1

When the order of the polynomial in the numerator is one degree higher than the degree of the polynomial in the denominator the rational function becomes asymptotic to the line obtained when the division is performed. You can use either long division or synthetic division but either way you will get y = (-2/3)x. (The remainder is ignored.) So you can see that as x approaches infinity y which is f(x), will approach negative infinity and vice versa.

Answer 2

For a large value of x what is the value of 3 - 2x²?