15. \( \lim _{x \rightarrow 4} \frac{v^{2}-6 v+8}{2 v^{2}-8 v} \) 16. \( \lim _{x \rightarrow 3} \frac{x^{2}-8 x+15}{x^{2}-7 x+12} \) 17. \( \lim _{h \rightarrow \frac{1}{2}} \frac{4 h^{2}+4 h-3}{2 h-1} \) 18. \( \lim _{x \rightarrow \frac{2}{3}} \frac{3 x-2}{3 x^{2}-11 x+6} \) 19. \( \lim _{w \rightarrow-\frac{4}{3}} \frac{9 w^{2}+9 w-4}{3 w^{2}+7 w+4} \) 20. \( \lim _{y \rightarrow 6} \frac{2 y^{2}-15 y+18}{3 y^{2}-17 y-6} \) 21. \( \lim _{x \rightarrow 5} \frac{2 x^{2}-13 x+15}{x^{2}-x-20} \) 22. \( \lim _{x \rightarrow-\frac{1}{3}} \frac{9 x^{2}-1}{6 x^{2}+5 x+1} \) 23. \( \lim _{y \rightarrow-1} \frac{y+1}{y^{3}+1} \)

Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{y\rightarrow -1}\left(\frac{y+1}{y^{3}+1}\right)\) - step1: Reduce the fraction: \(\lim _{y\rightarrow -1}\left(\frac{1}{y^{2}-y+1}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{y\rightarrow -1}\left(1\right)}{\lim _{y\rightarrow -1}\left(y^{2}-y+1\right)}\) - step3: Evaluate: \(\frac{1}{\lim _{y\rightarrow -1}\left(y^{2}-y+1\right)}\) - step4: Evaluate: \(\frac{1}{3}\) Calculate the limit \( \lim_{x \rightarrow \frac{2}{3}} \frac{3 x-2}{3 x^{2}-11 x+6} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow \frac{2}{3}}\left(\frac{3x-2}{3x^{2}-11x+6}\right)\) - step1: Reduce the fraction: \(\lim _{x\rightarrow \frac{2}{3}}\left(\frac{1}{x-3}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{x\rightarrow \frac{2}{3}}\left(1\right)}{\lim _{x\rightarrow \frac{2}{3}}\left(x-3\right)}\) - step3: Evaluate: \(\frac{1}{\lim _{x\rightarrow \frac{2}{3}}\left(x-3\right)}\) - step4: Evaluate: \(\frac{1}{-\frac{7}{3}}\) - step5: Multiply by the reciprocal: \(-\frac{3}{7}\) Calculate the limit \( \lim_{v \rightarrow 4} \frac{v^{2}-6 v+8}{2 v^{2}-8 v} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{v\rightarrow 4}\left(\frac{v^{2}-6v+8}{2v^{2}-8v}\right)\) - step1: Reduce the fraction: \(\lim _{v\rightarrow 4}\left(\frac{v-2}{v\times 2}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{v\rightarrow 4}\left(v-2\right)}{\lim _{v\rightarrow 4}\left(v\times 2\right)}\) - step3: Evaluate: \(\frac{2}{\lim _{v\rightarrow 4}\left(v\times 2\right)}\) - step4: Evaluate: \(\frac{2}{8}\) - step5: Reduce the fraction: \(\frac{1}{4}\) Calculate the limit \( \lim_{x \rightarrow 3} \frac{x^{2}-8 x+15}{x^{2}-7 x+12} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow 3}\left(\frac{x^{2}-8x+15}{x^{2}-7x+12}\right)\) - step1: Reduce the fraction: \(\lim _{x\rightarrow 3}\left(\frac{x-5}{x-4}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{x\rightarrow 3}\left(x-5\right)}{\lim _{x\rightarrow 3}\left(x-4\right)}\) - step3: Evaluate: \(\frac{-2}{\lim _{x\rightarrow 3}\left(x-4\right)}\) - step4: Evaluate: \(\frac{-2}{-1}\) - step5: Divide the terms: \(2\) Calculate the limit \( \lim_{y \rightarrow 6} \frac{2 y^{2}-15 y+18}{3 y^{2}-17 y-6} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{y\rightarrow 6}\left(\frac{2y^{2}-15y+18}{3y^{2}-17y-6}\right)\) - step1: Reduce the fraction: \(\lim _{y\rightarrow 6}\left(\frac{2y-3}{3y+1}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{y\rightarrow 6}\left(2y-3\right)}{\lim _{y\rightarrow 6}\left(3y+1\right)}\) - step3: Evaluate: \(\frac{9}{\lim _{y\rightarrow 6}\left(3y+1\right)}\) - step4: Evaluate: \(\frac{9}{19}\) Calculate the limit \( \lim_{w \rightarrow -\frac{4}{3}} \frac{9 w^{2}+9 w-4}{3 w^{2}+7 w+4} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{w\rightarrow -\frac{4}{3}}\left(\frac{9w^{2}+9w-4}{3w^{2}+7w+4}\right)\) - step1: Reduce the fraction: \(\lim _{w\rightarrow -\frac{4}{3}}\left(\frac{3w-1}{w+1}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{w\rightarrow -\frac{4}{3}}\left(3w-1\right)}{\lim _{w\rightarrow -\frac{4}{3}}\left(w+1\right)}\) - step3: Evaluate: \(\frac{-5}{\lim _{w\rightarrow -\frac{4}{3}}\left(w+1\right)}\) - step4: Evaluate: \(\frac{-5}{-\frac{1}{3}}\) - step5: Multiply by the reciprocal: \(-5\left(-3\right)\) - step6: Use the rules for multiplication and division: \(5\times 3\) - step7: Multiply the numbers: \(15\) Calculate the limit \( \lim_{h \rightarrow \frac{1}{2}} \frac{4 h^{2}+4 h-3}{2 h-1} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{h\rightarrow \frac{1}{2}}\left(\frac{4h^{2}+4h-3}{2h-1}\right)\) - step1: Reduce the fraction: \(\lim _{h\rightarrow \frac{1}{2}}\left(2h+3\right)\) - step2: Rewrite the expression: \(\lim _{h\rightarrow \frac{1}{2}}\left(2h\right)+\lim _{h\rightarrow \frac{1}{2}}\left(3\right)\) - step3: Calculate: \(1+3\) - step4: Calculate: \(4\) Calculate the limit \( \lim_{x \rightarrow 5} \frac{2 x^{2}-13 x+15}{x^{2}-x-20} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow 5}\left(\frac{2x^{2}-13x+15}{x^{2}-x-20}\right)\) - step1: Reduce the fraction: \(\lim _{x\rightarrow 5}\left(\frac{2x-3}{x+4}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{x\rightarrow 5}\left(2x-3\right)}{\lim _{x\rightarrow 5}\left(x+4\right)}\) - step3: Evaluate: \(\frac{7}{\lim _{x\rightarrow 5}\left(x+4\right)}\) - step4: Evaluate: \(\frac{7}{9}\) Calculate the limit \( \lim_{x \rightarrow -\frac{1}{3}} \frac{9 x^{2}-1}{6 x^{2}+5 x+1} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow -\frac{1}{3}}\left(\frac{9x^{2}-1}{6x^{2}+5x+1}\right)\) - step1: Reduce the fraction: \(\lim _{x\rightarrow -\frac{1}{3}}\left(\frac{3x-1}{2x+1}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{x\rightarrow -\frac{1}{3}}\left(3x-1\right)}{\lim _{x\rightarrow -\frac{1}{3}}\left(2x+1\right)}\) - step3: Evaluate: \(\frac{-2}{\lim _{x\rightarrow -\frac{1}{3}}\left(2x+1\right)}\) - step4: Evaluate: \(\frac{-2}{\frac{1}{3}}\) - step5: Multiply by the reciprocal: \(-2\times 3\) - step6: Multiply the numbers: \(-6\) Aquí están los límites calculados para cada una de las expresiones: 15. \( \lim _{v \rightarrow 4} \frac{v^{2}-6 v+8}{2 v^{2}-8 v} = \frac{1}{4} \) o \( 0.25 \) 16. \( \lim _{x \rightarrow 3} \frac{x^{2}-8 x+15}{x^{2}-7 x+12} = 2 \) 17. \( \lim _{h \rightarrow \frac{1}{2}} \frac{4 h^{2}+4 h-3}{2 h-1} = 4 \) 18. \( \lim _{x \rightarrow \frac{2}{3}} \frac{3 x-2}{3 x^{2}-11 x+6} = -\frac{3}{7} \) o \( -0.\dot{4}2857\dot{1} \) 19. \( \lim _{w \rightarrow -\frac{4}{3}} \frac{9 w^{2}+9 w-4}{3 w^{2}+7 w+4} = 15 \) 20. \( \lim _{y \rightarrow 6} \frac{2 y^{2}-15 y+18}{3 y^{2}-17 y-6} = \frac{9}{19} \) 21. \( \lim _{x \rightarrow 5} \frac{2 x^{2}-13 x+15}{x^{2}-x-20} = \frac{7}{9} \) o \( 0.\dot{7} \) 22. \( \lim _{x \rightarrow -\frac{1}{3}} \frac{9 x^{2}-1}{6 x^{2}+5 x+1} = -6 \) 23. \( \lim _{y \rightarrow -1} \frac{y+1}{y^{3}+1} = \frac{1}{3} \) o \( 0.\dot{3} \) Si necesitas más detalles sobre algún cálculo específico, házmelo saber.