一、(50%) CALCULUS(解答題目須清楚完整，始得完全分數)1. (10%) Find the limit _x → 0^+ (1/x)^x

4. (10%) Let $$L(\sigma) = \prod_{i=1}^n \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{1}{2}\left(\frac{x_i - \mu}{\sigma}\right)^2}, \quad \sigma > 0$$ Where $\mu$ and $x_i, i = 1, 2, \dots, n$ are known values. Find the value of $\sigma$ at which $L(\sigma)$ has its maximum. (Skip any derivative test)