Limite de una Función con Valor Absoluto en el Denominador Límites Algebraicos Límite en un Punto

Summary

This video tutorial explains how to calculate the limit of the function f(x) = 5x / |x + 4| as x approaches -4. It emphasizes the need to analyze the right-hand and left-hand limits separately. By evaluating both limits, the instructor demonstrates that the limits approach negative infinity from both directions. As a result, the overall limit does not exist. The explanation includes a clear walkthrough of the function's behavior around -4 and a graphical interpretation of the limits. The video wraps up with a reminder to subscribe and share if the explanation was helpful.

Takeaways

• 😀 The script explains how to solve a limit problem involving the function f(x) = 5x / |x + 4| as x approaches -4.
• 😀 The function is not defined at x = -4 because it causes division by zero in the denominator.
• 😀 To determine if the limit exists, we need to check if the right-hand and left-hand limits are equal and finite.
• 😀 The absolute value function is broken into two cases: |x + 4| = x + 4 for x ≥ -4, and |x + 4| = -(x + 4) for x < -4.
• 😀 The script first calculates the right-hand limit as x approaches -4 from the positive side (x > -4).
• 😀 For the right-hand limit, the denominator approaches 0 positively, and the result is negative infinity.
• 😀 The script then calculates the left-hand limit as x approaches -4 from the negative side (x < -4).
• 😀 For the left-hand limit, the denominator also approaches 0 positively, and the result is again negative infinity.
• 😀 Both limits, from the left and the right, are equal to negative infinity, but this means the overall limit does not exist.
• 😀 The final conclusion is that the limit at x = -4 does not exist because the function approaches negative infinity from both sides.
• 😀 The script ends with a recommendation to revisit the explanation and subscribe or share if the viewer found it helpful.

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