Question

求教一个极限与导数的问题

Answer 1

lim(h->0) [f(x0+3h)-f(x0-h)]/h

=lim(h->0) [f(x0+3h)-f(x0)+f(x0)-f(x0-h)]/h

=lim(h->0) [f(x0+3h)-f(x0)]/h + lim(h->0)[f(x0)-f(x0-h)]/h

=3lim(h->0) [f(x0+3h)-f(x0)]/(3h) + lim(h->0)[f(x0-h)-f(x0)]/(-h)

=3f'(x0)+f'(x0)

=4f'(x0)

A=4f'(x0)