对于函数f(x)，设f’(0)＝1/2，求lim n→无穷

Question

如题所述

Answer 1

如图

Answer 2

f'(0)=½
∵lim(n→∞)[(f(2/n)-f(0)]/(2/n)

=lim(n→∞)[(f'(2/n)·(2/n)'-0]/(2/n)' 0/0型，洛必达
=½
∴lim(n→∞)[n³(f(2/n)-f(0)]³
=lim(n→∞)2³[(f(2/n)-f(0)]³/(2/n)³
=lim(n→∞)2³{[(f(2/n)-f(0)]/(2/n)}³
=2³·½³
=1本回答被网友采纳