函數f(x)在x=a處可導,則lim h→0 (f(a+3h)-f(a-h))÷2h=?

函數f(x)在x=a處可導,則lim h→0 (f(a+3h)-f(a-h))÷2h=?

=lim {f(a+3h)--f(a)+f(a)--f(a--h)}/2h
=lim 3/2*[f(a+3h)--f(a)]/(3h)+lim 1/2*[f(a--h)--f(a)/(--h)]
=3/2*f'(a)+1/2*f'(a)
=2f'(a)