Question

$lim \ \frac{e {}^{3x } - 1}{2x}$
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Answer 1

$lim \: \frac{ {e}^{3x} - 1 }{2x}$

$lim \: \frac{ {e}^{3x} - 1 }{3x} \times \frac{3}{2}$

$1 \times \frac{3}{2}$

$\frac{3}{2}$

Answer 2

that's easy

$lim \: \: \: \: \: \: ( \frac{ {e}^{3x} - 1 }{ \frac{3x \times 2}{3} } ) = \frac{3}{2} lim \: \: \: \: ( \frac{ {e}^{3x} - 1}{3x}) = \frac{3}{2}.(1) \\x = > 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = > 0$