$\begin{aligned} & =\lim _{x \rightarrow 1}\left(\lim _{y \rightarrow \infty} y\left(1+\frac{(x / y)}{1 !}+\frac{(x / y)^2}{2 !}+\frac{(x / y)^3}{3 !}+\ldots-1\right)\right) \\ & =\lim _{x \rightarrow 1}(x+0)=1+0=1 .\end{aligned}$