下列函数极限正确的是（）A. lim_(x to infty) (1 + x)^(1)/(x) = eB. lim_(x to 0) (sin x)/(x) = 1C. lim_(x to infty) (1 - (1)/(x))^x = eD. lim_(x to infty) (sin x)/(x) = 1

A. $\lim_{x \to \infty} (1 + x)^{\frac{1}{x}} = e$

B. $\lim_{x \to 0} \frac{\sin x}{x} = 1$

C. $\lim_{x \to \infty} \left(1 - \frac{1}{x}\right)^x = e$

D. $\lim_{x \to \infty} \frac{\sin x}{x} = 1$