Question

$limita \: cand \: x - > 0 \: din \: \frac{ {3}^{x} - 1}{ {x}^{2} + 3x}$

Answer 1

Salut,

$\lim\limits_{x\to 0}\dfrac{3^x-1}{x^2+3x}=\lim\limits_{x\to 0}\left(\dfrac{3^x-1}{x}\cdot\dfrac{x}{x^2+3x}\right)=\\\\\\=\lim\limits_{x\to 0}\left(\dfrac{3^x-1}{x}\cdot\dfrac{1}{x+3}\right)=ln3\cdot\dfrac{1}{0+3}=\dfrac{ln3}3.$

Green eyes.