(1)
lim
△h→0
f(a+3h)?f(a?h)
2h=
lim
h→0
f(a+3h)?f(a)+f(a)?f(a?h)
2h
=
lim
h→0
f(a+3h)?f(a)
2h+
lim
h→0
f(a)?f(a?h)
2h
=[3/2
lim
h→0
f(a+3h)?f(a)
3h+
1
2
lim
h→0
f(a?h)?f(a)
?h]
=[3/2f′ (a)+
1
2f′(a)=2b.
(2)
lim
△h→0
f(a+h2)?f(a)
h]=
lim
h→0[
(a+h2) ?f(a)
h2h]
=
lim
h→0
f(a+h2) ?f(a)
h2?
lim
h→0h=f′(a)?0=0.