Why does Lim e ^ 1 / (x-1) x tend to be 1 left (1-0) = 0 instead of equal to + infinity

Why does Lim e ^ 1 / (x-1) x tend to be 1 left (1-0) = 0 instead of equal to + infinity

x→1-,x-1→0-,e^1/(x-1)→e^(-∞)=0