Problem - 4584
Calculate $\displaystyle\lim_{x\to 0^+}x^x$.
By the conclusion of # 4583, we have $\displaystyle\lim_{x\to 0^+}x\ln{x}=0$. Then
$$\lim_{x\to 0^+}x^x = \lim_{x\to 0^+}e^{x\ln{x}}=e^0 = \boxed{1}$$
Calculate $\displaystyle\lim_{x\to 0^+}x^x$.
By the conclusion of # 4583, we have $\displaystyle\lim_{x\to 0^+}x\ln{x}=0$. Then
$$\lim_{x\to 0^+}x^x = \lim_{x\to 0^+}e^{x\ln{x}}=e^0 = \boxed{1}$$