谁来为我解答这道高数题f(a)=1,f'(a)=2.求lim[f(a+1/n)/f(a)]的n次方（n趋向于正无穷

Question

谁来为我解答这道高数题
f(a)=1,f'(a)=2.求lim[f(a+1/n)/f(a)]的n次方（n趋向于正无穷

Answer 1

解为：e平方
具体解为：将上述转化为lim(1+1/n)的n次方形式.{1+(f(a+1/n)-f(a))/f(a)}的f(a)/[f(a+1/n)-f(a)]*[f(a+1/n)-f(a)]/[f(a)*(1/n)],可以得e的lim[f(a+1/n)-f(a)]/(1/n)次方,而[f(a+1/n)-f(a)]/(1/n)的n趋向于正无穷,则就是f'(a)=lim[f(a+1/n)-f(a)]/(1/n),最终结果为e的平方.