Evaluate $\lim_{s\to0}\frac{s\sqrt{e^s}}{e^s-1}$ without using L'Hospital rule.
I've done this: Since $\sqrt{e^s}\to1$as $s\to1$, so $\lim_{s\to0}\frac{s\sqrt{e^s}}{e^s-1}=\lim_{s\to0}\frac{s}{e^s-1}=1$
Are my steps correct? Is step 1 to step 2 available? Thank you.