How do you find the value of lim 2+3x-2x^4 / (3-5x)^3 as x approaches infinity?

Answer 1

Actually, the answer is POSITIVE infinity. The reason being that for sufficiently large x, the both the numerator and the denominator will be negative, so their quotient will be an increasingly large positive number.

Answer 2

I assume you mean lim (2+3x-2x^4) / (3-5x)^3 as x goes to infinity.

The answer is negative infinity.

To see this, we note that the numerator is a fourth degree polynomial, and the bottom is only a third degree polynomial.

Thus the x^4 term on the top "dominates" the polynomial on the bottom, and by this I mean that the x^4 term goes to infinity a lot faster than the bottom. And since the overall function is getting increasingly positive, the answer is positive infinity. (Updated...)