lim(x->0) ∫(0->x) [ 4sint+ t^2.cos(1/t) ]dt/ [(1+cosx) ∫(0->x) ln(1+t) dt]
=(1/2)lim(x->0) ∫(0->x) [ 4sint+ t^2.cos(1/t) ]dt/ ∫(0->x) ln(1+t) dt
洛必達
=(1/2)lim(x->0) [ 4sinx+ x^2.cos(1/x) ]/ ln(1+x)
=(1/2)lim(x->0) [ 4sinx+ x^2.cos(1/x) ]/ x
=(1/2)lim(x->0) [ 4sinx/x + x.cos(1/x) ]
=4+0
=4