Question

calcule lim x → 0 ( 1/5 - 1/5-x )/ x

Answer 1

Resposta:

Explicação passo-a-passo:

$\lim_{x \to 0}\dfrac{\frac{1}{5}-\frac{1}{5-x}}{x}=\lim_{x \to 0}\dfrac{\frac{5-x-5}{5(5-x)}}{x}=\lim_{x \to 0}\dfrac{\frac{-x}{5(5-x)}}{x}=\\\\=\lim_{x \to 0}\dfrac{-x}{5(5-x)}.\dfrac{1}{x}=\lim_{x \to 0}\dfrac{-1}{5(5-x)}=$

$=\dfrac{-1}{5(5-0)}=\dfrac{-1}{5.5}=-\dfrac{1}{25}$