Cálculo: Límites

Data Science – Mcoder.ai


El Cálculo aparece en numerosos lugares de la ciencia de datos, se esconde detrás de la sencilla solución analítica de un problema de mínimos cuadrados ordinarios en regresión lineal o incrustado en cada propagación hacia atrás que una red neuronal hace para aprender un nuevo patrón.

Se dice que una función f (x) tiene límite L en el punto x = a, si es posible aproximar f (x) a L tanto como se quiera cuando x se acerca indefinidamente a a, siendo distinto de a.

Dado el punto a, y según la anterior definición, existen dos formas de aproximar x a a: desde valores x > a (por la derecha) y desde valores x < a (por la izquierda). En cada caso se obtienen valores denominados límite por la derecha (x→a+) y límite por la izquierda (x→a-). Por definición, para que exista el límite de una función ha de cumplirse que existan los dos límites laterales (por la derecha y por la izquierda) y que ambos sean iguales.

¿Cómo calcular un límite?

A veces al hacer esta sustitución el resultado es una indeterminación, esto es una operación algebraica que no podemos predecir su resultado, como las siguientes:

Existen diferentes procedimientos para resolver estas indeterminaciones, la más común es factorizar la función para luego sustituir y poder obtener un resultado, por ejemplo:

Como tal en R no se tiene una función que calcule límites, están otros conceptos más utilizados como por ejemplo las derivadas, de lo cual hablaremos en el siguiente post ¡No te lo pierdas!

Data Science – Mcoder.ai

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