題目 Problem Let f(x)=limn→∞(1+xn)nf(x)=\lim_{n\to\infty}\left(1+\frac{x}{n}\right)^nf(x)=limn→∞(1+nx)n. Then which of the following is true? (a) f(x)f(x)f(x) does not exist. (b) f(x)=∑n=0∞xnf(x)=\sum_{n=0}^{\infty}x^nf(x)=∑n=0∞xn. (c) f(x)=∑n=0∞xnn!f(x)=\sum_{n=0}^{\infty}\dfrac{x^n}{n!}f(x)=∑n=0∞n!xn. (d) f(x)=exf(x)=e^xf(x)=ex. (e) None of the above. 解答 待補。
