Question

高等数学求极限问题

求解答

Answer 1

lim nf(a-1/n) = lim f(a-1/n)/(1/n) (0/0型,洛必达) = lim f'(a-1/n) 1/n*n/(-1/n*n) = -lim f'(a-1/n)=-1

Answer 2

f（a-1/n) ~ f(a)-f'(a)/n = -f'(a)/n

带入得到lim n f(a-1/n) = lim n * [-f'(a)]/n = -f'(a)=-1