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:**
  

Explore the limit \(\lim_{x \to +\infty} \frac{x^3 - 3x^2 + 1}{-2x^2 + 3}\) with a detailed step-by-step solution. Understand the behavior of polynomials and limits as x approaches infinity. Suitable for advanced high school students and college-level calculus enthusiasts.

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