\lim_{x \to 0-}\frac{\ x+e^{ \frac{1}{x}}}{x} = 1 + \lim_{x \to 0-}\frac{\ e^{ \frac{1}{x}}}{x} = 1 - \lim_{x \to 0+}\frac{\ e^{ -\frac{1}{x}}}{x} = 1 - \lim_{x \to 0+}\frac{1}{xe^{ \frac{1}{x}}} = 1 - \lim_{x \to +\infty}\frac{x}{e^x} = 1 - \lim_{x \to +\infty}\frac{1}{e^x} = 1