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Evaluate the limit

Evaluate

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


The numerator and denominator are both continuous since they are polynomials. Since x^2 + 2ax + a^2 is non-zero we may then apply Theorem 3.2 to compute the limit,

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

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