Question

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

• A. $\log 2$
• B. $\log 4$
• C. $\frac{1}{2}\log 2$
• D. $0$

Answer 1

The correct option is B $\log 4$

Form of the limit is $\frac{0}{0}$

Thus using L-hospital rule,

$\underset{x\to 0}{lim}\frac{2^x-1}{\sqrt{1+x}-1}=\underset{x\to 0}{lim}\frac{2^x\log 2}{\frac{1}{2\sqrt{1+x}}}=2\log 2$