Question

Evaluate: $\underset{x\to 0^{-}}{lim}\left(\frac{1}{1+2^{1/x}}\right)$

Answer 1

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

As $x$ is negative, $\frac{1}{x}\to -\infty$

So, $2^{1/x}\to (1/2{)}^{\infty }=0$

sO, ${lim}_{x\to 0^{-}}\frac{1}{1+0}=1$