Find the Value of Constant a for the Limit to Exist

Math Problem Statement

español

Halle el valor o los valores de la constante a para que lim (x→1) f(x) exista, donde f(x) = {ax^2 + 2x si x ≤ 1, x^3 - 1 si x > 1}.

El problema solicita encontrar el valor o los valores de la constante $a$ para que el límite de la función $f(x)$ exista cuando $x \to 1$ , dado que:

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Limits
Continuity
Piecewise Functions

Limit of a function as x approaches a point
Equality of left-hand and right-hand limits

Definition of continuity at a point
Properties of limits

Grades 10-12

Finding the Constant a for Limit of Piecewise Function to Exist

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Find the Constant 'a' for Continuity in a Piecewise Function

Determining the Constant 'a' for Continuity of a Piecewise Function

Finding Continuity for a Piecewise Function at x = 0