有界量和无穷小的乘积为无穷小1)利用函数极限和数列极限的关系。n->∞时,nπ->∞,sinnπ ->0,令x=1/nπ则lim x->0 [sin(1/x)]/x =lim x->+∞ [cos(1/x)]*(-1/x²)=lim x->+∞ [-x²cos(1/x)]=02)lim x->a {sin[1/(x-a)]}/(x-a) =lim x->a cos{1/[x-a]}*[-1/(x-a)²]=-lim x->a (x-a)²cos{1/[x-a]}=0