求极限limx→∞x2[1-cos(5/x)].

求极限limx→∞x2[1-cos(5/x)].
【正确答案】：令t=1/x,则原式=limx→0{[1-cos(5/x)/(1/x2)]} =limt→0[(1-cos5t)/t2] =limt→0(5sin5t/2t)=25/2．