根据同阶无穷小,x→0时,sinx～x
lim(x→0)cos(sinx)-cosx/x^4
=lim(x→0)cosx-cosx/x^4
=lim(x→0)cosx(1-1/x^4)
=lim(x→0)cosx*lim(x→0)(1-1/x^4)
=1*lim(x→0)(1-1/x^4)
=-∞