若函数f(x)在点x=a处可导,则lim(h→0)[f(a+4h)-f(a-2h)]/3h=?
问答/228℃/2025-01-15 14:49:15
优质解答：
把h趋于0写作h--0
lim(h--0)[f(a+4h)-f(a-2h)]/3h
=lim(h--0)[f(a+4h)-f(a)+f(a)-f(a-2h)]/3h
=lim(h--0)(4/3)[f(a+4h)-f(a)]/4h+lim(h--0)(2/3)[f(a)-f(a-2h)]/2h
=(4/3)f'(a)+(2/3)f'(a)
=2f'(a)