Verify the Continuity of a Piecewise Function at Specific Points

Math Problem Statement

Explica pas cu pas rezolvarea

Studiati continuitatea functiilor urmatoare in punctele specificate: f: R -> R, f(x) = { 0, x <= 1; 1, x > 1 } in x0 = 1 si x1 = 2.

Solution

Pentru a rezolva cerința, trebuie să verificăm continuitatea funcției $f(x)$ în punctele specificate, $x_0 = 1$ și $x_1 = 2$ . Să analizăm pașii:

1. Definiția funcției

Funcția dată este:

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Math Problem Analysis

Mathematical Concepts

Continuity
Piecewise Functions
Limits
Lateral Limits

Formulas

Definition of continuity: f(x0) exists, lim_{x -> x0} f(x) exists, and lim_{x -> x0} f(x) = f(x0)
Lateral limits: lim_{x -> x0^-} f(x) and lim_{x -> x0^+} f(x)

Theorems

Continuity Definition

Suitable Grade Level

Grades 10-12

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