PART 7：例題-不定型 \(\frac{0}{0}\)

求極限 \(\lim\limits_{x \to 0} \frac{{{e^{3x}} - 1}}{x}\)

SOL :

代 \(x = 0\) 入極限得 \(\frac{0}{0}\) ， \(\lim\limits_{x \to 0} \frac{{{e^{3x}} - 1}}{x}\) \(\ \overset{L}{\mathop{=}}\,\ \) \(\lim\limits_{x \to 0} \frac{{3{e^{3x}}}}{1}\) ，

代 \(x = 0\) 入極限得 \(\lim\limits_{x \to 0} \frac{{3{e^0}}}{1} = 3\)