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For \( \alpha = 2 \), \( \displaystyle\lim_{x \to x_0} \left| \dfrac{g(x) + e^{x_0}}{x - x_0} \right| = 0 \)

For \( \alpha = 2 \), \( \displaystyle\lim_{x \to x_0} \left| \dfrac{g(x) + e^{x_0}}{x - x_0} \right| = 1 \)

For \( \alpha = 3 \), \( \displaystyle\lim_{x \to x_0} \left| \dfrac{g(x) + e^{x_0}}{x - x_0} \right| = 0 \)

For \( \alpha = 3 \), \( \displaystyle\lim_{x \to x_0} \left| \dfrac{g(x) + e^{x_0}}{x - x_0} \right| = \dfrac{2}{3} \)