Question

若f(x)为连续函数,且f(0)=1,f(1)=0,则limx→无穷 f(x sin1/x)=?

Answer 1

当 x--> ∞时,1/x-->0 ,

xsin1/x=sin(1/x)/(1/x) ---> 1

limx→无穷 f(x sin1/x)=f(1)=0