1. **Statement of the problem:** Given the function $$f(x) = \frac{x^3 - 2x + 1}{(x+1)^2}$$ defined on $$\mathbb{R} \setminus \{-1\}$$, we are asked to calculate the limits of $$f$$ at the boundaries of its domain. 2. **Calculate the limits at the boundaries:** - As $$x \to -1$$, the denominator $$ (x+1)^2 \to 0$$, so we check the behavior of the numerator: $$x^3 - 2x + 1 = (-1)^3 - 2(-1) + 1 = -1 + 2 + 1 = 2$$ Since numerator approaches 2 and denominator approaches 0 from the positive side (square), the limit tends to $$+\infty$$ or $$+\infty$$ from both sides. - As $$x \to +\infty$$: $$f(x) \approx \frac{x^3}{x^2} = x \to +\infty$$ - As $$x \to -\infty$$: $$f(x) \approx \frac{x^3}{x^2} = x \to -\infty$$ **Final limits:** $$\lim_{x \to -1} f(x) = +\infty$$ $$\lim_{x \to +\infty} f(x) = +\infty$$ $$\lim_{x \to -\infty} f(x) = -\infty$$