已知f(a)=0,f '(a)=1,则lim(n→∞)nf(a-1/n)=?
问题描述:
已知f(a)=0,f '(a)=1,则lim(n→∞)nf(a-1/n)=?
答
lim(n→∞)nf(a-1/n)
=lim(n→∞)[f(a-1/n)-f(a)]/(1/n)
=-lim(n→∞)[f(a-1/n)-f(a)]/(-1/n)
=-f'(a)
=-1