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Actividad 1. Determinar: \( \lim _{x \rightarrow 2}\left(x^{2}+x+7\right) \)

Ask by Howell Wheeler. in Ecuador
Mar 14,2025

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El límite es 13.

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Para encontrar el límite \( \lim _{x \rightarrow 2}\left(x^{2}+x+7\right) \), simplemente sustituimos el valor de \( x \) por 2 en la expresión. Así que: \[ \lim _{x \rightarrow 2}\left(x^{2}+x+7\right) = 2^{2}+2+7 = 4 + 2 + 7 = 13 \] Por lo tanto, el límite es 13. Para reforzar nuestra comprensión, es interesante notar que los límites son fundamentales en el cálculo y aparecen en el análisis de funciones, lo que es crucial para entender conceptos más avanzados como la continuidad y la derivación. Evaluar límites de funciones polinómicas es particularmente sencillo, ya que se pueden calcular simplemente sustituyendo el valor. Además, es común cometer el error de no considerar el tipo de función con la que se trabaja. Siempre hay que recordar que algunas funciones tienen comportamientos diferentes al acercarse al límite, especialmente en funciones racionales o con raíces. Verificar la continuidad puede ahorrar mucho tiempo y confusión.

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