Question

Evaluate: $\underset{n\to 0}{lim}\frac{2^{\frac{1}{n}}-1}{2^{\frac{1}{n}}+1}$

• A. $1$
• B. $\frac{1}{2}$
• C. $-1$
• D. $0$

Answer 1

The correct option is A $1$

$\underset{n\to 0}{lim}\frac{2^{\frac{1}{n}}-1}{2^{\frac{1}{n}}+1}=\underset{n\to 0}{lim}\frac{(2^{\frac{1}{n}}+1)-2}{2^{\frac{1}{n}}+1}$

$=\underset{n\to 0}{lim}1-\frac{2}{2^{\frac{1}{n}}+1}=1-\frac{2}{2^{\frac{1}{n}}+1}$

$=1-\frac{2}{\infty +1}=1-\frac{2}{\infty }=1-0$

$=1$