II. Calcula los siguientes limites \( \begin{array}{ll}\text { 1. } \operatorname{Lim}_{x \rightarrow 2}\left(\frac{x^{3}+2 x+3}{x^{2}+5}\right) & \text { 6. } \operatorname{Lim}_{x \rightarrow 1}\left(\frac{4 x-1}{2 x^{2}-3 x+4}\right) \\ \text { 2. } \operatorname{Lim}_{x \rightarrow-1}\left(\frac{2 x+1}{x^{2}-3 x+4}\right) & \text { 7. } \operatorname{Lim}_{x \rightarrow 3}\left(\frac{3 x^{2}-1}{4 x^{2}+2}\right) \\ \text { 3. } \operatorname{Lim}_{x \rightarrow-3}\left(\frac{x^{2}-9}{2 x^{2}+7 x-3}\right) & \text { 8. } \lim _{x \rightarrow-5}\left(\frac{x^{3}-5}{3 x^{3}+x^{2}-5}\right) \\ \text { 4. } \operatorname{Lim}_{x \rightarrow 4}\left(\frac{x^{2}-4 x+1}{3 x^{2}-2 x+1}\right) & \text { 9. } \operatorname{Lim}_{x \rightarrow 0}\left(\frac{x^{3}-4 x^{2}+x-1}{2 x^{2}+4 x-1}\right) \\ \text { 5. } \operatorname{Lim}_{x \rightarrow 0}\left(\frac{x^{2}-3 x}{x+1}\right) & \end{array} \)

Aquí tienes los límites de las funciones que mencionaste: 1. \(\operatorname{Lim}_{x \rightarrow 2}\left(\frac{x^{3}+2 x+3}{x^{2}+5}\right) = \frac{2^3 + 2(2) + 3}{2^2 + 5} = \frac{8 + 4 + 3}{4 + 5} = \frac{15}{9} = \frac{5}{3}\) 2. \(\operatorname{Lim}_{x \rightarrow -1}\left(\frac{2 x+1}{x^{2}-3 x+4}\right) = \frac{2(-1)+1}{(-1)^{2} -3(-1) + 4} = \frac{-2+1}{1 + 3 + 4} = \frac{-1}{8}\) 3. \(\operatorname{Lim}_{x \rightarrow -3}\left(\frac{x^{2}-9}{2 x^{2}+7 x-3}\right) = \frac{(-3)^{2}-9}{2(-3)^{2}+7(-3)-3} = \frac{9-9}{18-21-3} = \frac{0}{-6} = 0\) 4. \(\operatorname{Lim}_{x \rightarrow 4}\left(\frac{x^{2}-4 x+1}{3 x^{2}-2 x+1}\right) = \frac{4^{2}-4(4)+1}{3(4)^{2}-2(4)+1} = \frac{16 - 16 + 1}{48 - 8 + 1} = \frac{1}{41}\) 5. \(\operatorname{Lim}_{x \rightarrow 0}\left(\frac{x^{2}-3 x}{x+1}\right) = \frac{0^{2}-3(0)}{0+1} = \frac{0}{1} = 0\) 6. \(\operatorname{Lim}_{x \rightarrow 1}\left(\frac{4 x-1}{2 x^{2}-3 x+4}\right) = \frac{4(1)-1}{2(1)^{2}-3(1)+4} = \frac{4-1}{2-3+4} = \frac{3}{3} = 1\) 7. \(\operatorname{Lim}_{x \rightarrow 3}\left(\frac{3 x^{2}-1}{4 x^{2}+2}\right) = \frac{3(3)^{2}-1}{4(3)^{2}+2} = \frac{27-1}{36+2} = \frac{26}{38} = \frac{13}{19}\) 8. \(\lim _{x \rightarrow-5}\left(\frac{x^{3}-5}{3 x^{3}+x^{2}-5}\right) = \frac{(-5)^{3}-5}{3(-5)^{3}+(-5)^{2}-5} = \frac{-125-5}{-375+25-5} = \frac{-130}{-355} = \frac{130}{355} = \frac{26}{71}\) 9. \(\operatorname{Lim}_{x \rightarrow 0}\left(\frac{x^{3}-4 x^{2}+x-1}{2 x^{2}+4 x-1}\right) = \frac{0^{3}-4(0)^{2}+0-1}{2(0)^{2}+4(0)-1} = \frac{-1}{-1} = 1\) Puedes usar estos resultados para seguir practicando límites y mejorar tus habilidades en cálculo. ¡Diviértete!