Note that the exponential is a continuous function. Therefore, if lim x → 0 + x l n ( x ) {\displaystyle \displaystyle {\lim _{x\rightarrow 0^{+}}}xln(x)} exists, the following equality would hold:
lim x → 0 + e x l n ( x ) = e ( lim x → 0 + x l n ( x ) ) . {\displaystyle \displaystyle {\lim _{x\rightarrow 0^{+}}}e^{xln(x)}=e^{\left(\displaystyle {\lim _{x\rightarrow 0^{+}}}xln(x)\right)}.}
exists, the following equality would hold:
