Math Problem Statement

limx→+∞x3−3x2+1−2x2+3=

Solution

To solve the limit limx+x33x2+12x2+3\lim_{x \to +\infty} \frac{x^3 - 3x^2 + 1}{-2x^2 + 3}, we can analyze the behavior of the expression as xx approaches infinity.

Step-by-Step Solution:

  1. Identify the degrees of the polynomials:

    • The numerator x33x2+1x^3 - 3x^2 + 1 is a polynomial of degree 3.
    • The denominator 2x2+3-2x^2 + 3 is a polynomial of degree 2.
  2. Divide both the numerator and the denominator by the highest power of xx in the denominator: