lim[cos[1/x]/x,x→0],
设t = 1/x 则
lim[cos[1/x]/x,x→0]
=lim[t*cost,t→∞],
设t=2nπ,
lim[t*cost,t→∞]
=lim[t*cos[2nπ],n→∞]
=lim[t,n→∞]
= ∞
设t= (2n+1/2)π,
lim[tcost,t→∞]
=lim[t*cos[(2n+1/2)π],n→∞]
= 0,
所以极限不存在.