Learn how to solve integrals with radicals problems step by step online. Find the limit of (-4+4x-x^2)/(3x^2-x^3+-4) as x approaches 2. For easier handling, reorder the terms of the polynomial -x^3+3x^2-4 from highest to lowest degree. We can factor the polynomial -x^3+3x^2-4 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -4. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial -x^3+3x^2-4 will then be.

Find the limit of (-4+4x-x^2)/(3x^2-x^3+-4) as x approaches 2