Question

limite 3^x-1
x->0 6^x-1

Answer 1

Explicação passo-a-passo:

Calcular limite:

$\sf \lim_{x \to 0} \dfrac{3^{x-1}}{6^{x-1}}$

$\sf \lim_{x \to 0} \dfrac{3^{0-1}}{6^{0-1}}$

$\sf \lim_{x \to 0} \dfrac{3^{-1}}{6^{-1}}$

$\sf \lim_{x \to 0} \dfrac{3^{-1}}{2^{-1} \cdot 3^{-1}}$

$\sf \lim_{x \to 0} \dfrac{\diagup{ \!\!\!3^{-\diagup \!\!\!1}}}{2^{-1} \cdot \diagup \!\!\!{3^{-\diagup \!\!\!1}}}$

$\sf \lim_{x \to 0} \dfrac{1}{2^{-1}}$

$\sf \lim_{x \to 0} \dfrac{2^1}{1}$

$\sf \lim_{x \to 0} \boxed{ 2}$