limx趋近0(1/x)cos(1/x)的极限

Question

limx趋近0(1/x)cos(1/x)的极限

Answer 1

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...