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Question
\[\lim_{x \to 0} \frac{e^{3x} - e^{2x}}{x}\]
Solution
\[\lim_{x \to 0} \left[ \frac{e^{3x} - e^{2x}}{x} \right]\]
\[ = \lim_{x \to 0} \left[ \left( \frac{e^{3x} - 1}{x} \right) - \left( \frac{e^{2x} - 1}{x} \right) \right]\]
\[ = \lim_{x \to 0} \left[ 3\left( \frac{e^{3x} - 1}{3x} \right) - 2\left( \frac{e^{2x} - 1}{2x} \right) \right]\]
\[ = 3 \times 1 - 2 \times 1\]
\[ = 1\]
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