Question

$\underset{x\to 0^{-}}{lim}\frac{1}{3-2^{1/x}}$ is equal to :

• A. $0$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$
• E. $-\infty$

Answer 1

The correct option is D $\frac{1}{3}$

We need to find limit of $\underset{x\to 0^{-}}{lim}\frac{1}{3-2^{1/x}}$
Put $x=0-h$
Therefore, $\underset{h\to 0}{lim}\frac{1}{3-2^{\frac{1}{0-h}}}$
$=\underset{h\to 0}{lim}\frac{1}{3-2^{-\frac{1}{h}}}$
$=\frac{1}{3-2^{-\frac{1}{0}}}=\frac{1}{3-2^{-\infty }}$
$=\frac{1}{3-0}=\frac{1}{3}$