Bài tập 48 trang 112 SGK Toán 12 NC

Bài tập 48 trang 112 SGK Toán 12 NC

a)

\(\begin{array}{l}
\mathop {\lim }\limits_{x \to 0} \frac{{{e^2} - {e^{3x + 2}}}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{{{e^2}\left( {1 - {3^{3x}}} \right)}}{x}\\
 =  - 3{e^2}.\mathop {\lim }\limits_{x \to 0} \frac{{{e^{3x}} - 1}}{{3x}} =  - 3{e^2}
\end{array}\)

b)

\(\begin{array}{l}
\mathop {\lim }\limits_{x \to 0} \frac{{{e^{2x}} - {e^{5x}}}}{x}\\
 = \mathop {\lim }\limits_{x \to 0} \left( {\frac{{{e^{2x}} - 1}}{x} - \frac{{{e^{5x}} - 1}}{x}} \right)\\
 = 2 - 5 =  - 3
\end{array}\)

-- Mod Toán 12