⛔️ Cómo calcular LIMITES LATERALES FUNCIÓN POR PARTES - FUNCIÓN A TROZOS| Juliana la profe

Summary

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Takeaways

• 😀 The lesson covers how to calculate lateral limits in a piecewise function.
• 😀 The function in question has three different rules for different intervals of x.
• 😀 The task is to check if the limit of the function exists as x approaches 1 and 3.
• 😀 The first step involves mapping the function’s intervals on a number line with critical values at x = 1 and x = 3.
• 😀 For x < 1, the function is defined as f(x) = x².
• 😀 For 1 ≤ x < 3, the function is defined as f(x) = x.
• 😀 For x ≥ 3, the function is defined as f(x) = 3 - x.
• 😀 To check if the limit at x = 1 exists, evaluate both the left-hand limit (x²) and right-hand limit (x). Both limits give the value 1, so the limit exists and equals 1.
• 😀 To check if the limit at x = 3 exists, evaluate the left-hand limit (x) and right-hand limit (3 - x). The left-hand limit is 3, and the right-hand limit is 0, so the limits are not equal, and the limit at x = 3 does not exist.
• 😀 The main theorem states that a limit exists when both left-hand and right-hand limits are equal.
• 😀 The conclusion is that the limit of the function as x approaches 1 exists and equals 1, while the limit as x approaches 3 does not exist.

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