lim(x趋向0)[x^2-sin^2x]/x^4怎么求?为什么不能用lim(x->a)[f(x)-g(x)]=lim(x->a)f(x)-lim(x->a)g(x)?

Question

lim(x趋向0)[x^2-sin^2 x]/x^4怎么求?
为什么不能用
lim(x->a)[f(x)-g(x)]=lim(x->a)f(x)-lim(x->a)g(x)?

Answer 1

lim(x->0)[x^2-(sinx)^2]/x^4 (0/0)
=lim(x->0)[2x-sin2x]/(4x^3) (0/0)
=lim(x->0)[2-2cos2x]/(12x^2)
=lim(x->0)[1-cos2x]/(6x^2) (0/0)
=lim(x->0)[2sin2x]/(12x)
=(1/3)lim(x->0)[sin2x]/(2x)
=1/3