Question
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Answer
El límite es 0.
Solution
Para resolver el límite:
\[ \lim _{y \rightarrow-1} \frac{y^{2}-1}{y+2} \]
Primero, evaluamos directamente sustituyendo \( y = -1 \):
1. **Sustitución en el numerador:**
\[
y^{2} - 1 = (-1)^{2} - 1 = 1 - 1 = 0
\]
2. **Sustitución en el denominador:**
\[
y + 2 = -1 + 2 = 1
\]
Entonces, el límite se reduce a:
\[
\frac{0}{1} = 0
\]
Por lo tanto, el límite es:
\[
\boxed{0}
\]
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Simplify this solution Beyond the Answer
To find the limit \( \lim _{y \rightarrow-1} \frac{y^{2}-1}{y+2} \), we can begin by substituting \( y = -1 \) directly into the expression. First, we calculate the numerator: \[ y^2 - 1 = (-1)^2 - 1 = 1 - 1 = 0 \] Next, we calculate the denominator: \[ y + 2 = -1 + 2 = 1 \] So, we have: \[ \frac{y^2 - 1}{y + 2} = \frac{0}{1} = 0 \] Therefore, \[ \lim _{y \rightarrow-1} \frac{y^{2}-1}{y+2} = 0 \]
