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Actividad 4. Determinar: \( \lim _{x \rightarrow \infty} \frac{37}{(x+9)^{2}} \)

Ask by Hodges Stewart. in Ecuador
Mar 15,2025

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El límite de \( \frac{37}{(x+9)^2} \) cuando \( x \) tiende a \( \infty \) es \( 0 \).

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¡Vamos a resolver este límite juntos! Cuando \(x\) tiende a infinito, el término \( (x + 9)^2 \) también crece sin límites, lo que significa que el denominador se hace muy grande. Como la función que estamos considerando es \( \frac{37}{(x + 9)^2} \), a medida que el denominador se vuelve enorme, el resultado de la fracción se va acercando a cero. Por lo tanto, podemos concluir que: \[ \lim _{x \rightarrow \infty} \frac{37}{(x+9)^{2}} = 0. \] ¡Y ahí lo tienes! El límite es cero.

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