企源知识库

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