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**1.** Graficar en GeoGebra la siguiente función a trozos, y de acuerdo con ella determinar los límites laterales dados, presentar la gráfica y la respuesta a cada inciso.

To solve this problem, let's first examine the piecewise function \( f(x) \) and understand the limits at the specified points.

### Function Definition:
The function \( f(x) \) is defined as follows:
\[
f(x) = \begin{cases} 
x + 2 & \text{if } x \leq -1 \\
-x^2 + 2x & \text{if } -1 < x < 1 \\
\frac{1}{x} & \text{if } x > 1 
\end{cases}
\]

### Problem Requirements:
We need to evaluate the following limits:
1. \( \lim_{x \to -1^-} f(x) \) (left-hand limit as \( x \to -1 \))
2. \( \lim_{x \to -1^+} f(x) \) (right-hand limit as \( x \to -1 \))
3. \( \lim_{x \to 1^-} f(x) \) (left-hand limit as \( x \to 1 \))
4. \( \lim_{x \to 1^+} f(x) \) (right-hand limit as \( x \to 1 \))

I'll go through each limit analytically and then generate a GeoGebra graph for visualization.

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### Solution:

1. **Limit as \( x \to -1^- \):**  
   For \( x \to -1^- \), we use the piece \( f(x) = x + 2 \).  
   \[
   \lim_{x \to -1^-} f(x) = (-1) + 2 = 1
   \]

2

Graficar en GeoGebra la siguiente función a trozos, y de acuerdo con ella determinar los límites laterales dados, presentar la gráfica y la respuesta a cada inciso.

Learn how to analyze the left and right limits of a piecewise function with a step-by-step approach. This problem explores limit concepts, focusing on the limits as x approaches -1 and 1 from both sides.

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