D) \( \lim _{x \rightarrow+\infty} \frac{2 x-3 x^{2}}{5 x^{2}+7} \)

Calculate the limit \( \lim_{x\rightarrow+\infty} \frac{2x-3x^2}{5x^2+7} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow +\infty}\left(\frac{2x-3x^{2}}{5x^{2}+7}\right)\) - step1: Rewrite the expression: \(\lim _{x\rightarrow +\infty}\left(\frac{x^{2}\left(\frac{2}{x}-3\right)}{x^{2}\left(5+\frac{7}{x^{2}}\right)}\right)\) - step2: Reduce the fraction: \(\lim _{x\rightarrow +\infty}\left(\frac{\frac{2}{x}-3}{5+\frac{7}{x^{2}}}\right)\) - step3: Rewrite the expression: \(\frac{\lim _{x\rightarrow +\infty}\left(\frac{2}{x}-3\right)}{\lim _{x\rightarrow +\infty}\left(5+\frac{7}{x^{2}}\right)}\) - step4: Calculate: \(\frac{-3}{\lim _{x\rightarrow +\infty}\left(5+\frac{7}{x^{2}}\right)}\) - step5: Calculate: \(\frac{-3}{5}\) - step6: Calculate: \(-\frac{3}{5}\) La limitante de la expresión \( \frac{2x-3x^2}{5x^2+7} \) cuando \( x \) se acerca a \( +\infty \) es \( -\frac{3}{5} \) o aproximadamente \( -0.6 \).