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

Step-by-Step Solution:

1. Identify the degrees of the polynomials:

   • The numerator $x^3 - 3x^2 + 1$ is a polynomial of degree 3.
   • The denominator $-2x^2 + 3$ is a polynomial of degree 2.

2. Divide both the numerator and the denominator by the highest power of $x$ in the denominator: