φ(0)
=∫(0->1) f(0) dt
=f(0)
//
u=xt
du=xdt
t=0, u=0
t=1, u=x
lim(x->0) φ(x)
=lim(x->0) ∫(0->1) f(xt) dt
=lim(x->0) ∫(0->x) f(u) du /x
洛必达
=lim(x->0) f(x)
=f(0)
=φ(0)
x=0, φ(x) 连续
//
φ'(x)
=d/dx ∫(0->1) f(xt) dt
=d/dx [(1/x) ∫(0->x) f(t) dt]
= [xf(x) -∫(0->x) f(t) dt]/x^2
