Mathematics

Problem

For the piecewise function

p(x)=\begin{cases} \dfrac{2x}{x-1}, & x<1,\\ e^{x-1}-1, & x>1, \end{cases}

calculate

\displaystyle\lim_{x\to 1^-} p(x)

and

\displaystyle\lim_{x\to 1^+} p(x)