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Evaluate the limit

Evaluate

    \[ \lim_{a \to 0} \frac{x^2 - a^2}{x^2 + 2ax + a^2}, \qquad \text{for } x \neq 0. \]


Since the numerator and denominator are both polynomials, they are continuous. Since the denominator is non-zero for x \neq 0, we may apply Theorem 3.2 to conclude f/g is continuous. So, we can compute the limit,

    \[ \lim_{a \to 0} \frac{x^2-a^2}{x^2 + 2ax + a^2} = \frac{x^2}{x^2} = 1. \]

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