Analise as afirmativas abaixo:

1. I. $\underset{a\to 1}{\lim }\left(\frac{\sqrt{a}-1}{a-1}\right)=\frac{1}{2}$
   

2. II. $\underset{x\to 0}{\lim }\left(\sqrt[x]{\frac{k+x}{k-x}}\right)=e^{\frac{2}{k}}$
   

3. III. $\underset{x\to \frac{\pi }{2}}{\lim }\left(\frac{\mathrm{tg}2x}{x-\frac{\pi }{2}}\right)=1$
   

Assinale a alternativa correta: