Question-11

Find the value of the following limit:

\[ \begin{equation*} \lim\limits _{x\rightarrow 0^{+}} \ \ \frac{\sqrt{x}}{1-e^{2\sqrt{x}}} \end{equation*} \]

Answer

\(-0.5\)

Solution

We can use the standard limit: \(\displaystyle \lim\limits _{x\rightarrow 0} \ \frac{e^{x} -1}{x} =1\). To get the standard form, we need to multiply and divide by \(\displaystyle -2\) and notice that the inverse of the above function still has limit \(\displaystyle 1\).