企源知识库

求lim_x→∞x{√[1+sin(1/x)-1]}
【正确答案】：lim_x→∞x{√[1+sin(1/x)]-1}=lim_x→∞{{√[1+sin(1/x)]-1}/(1/x)} =lim_x→∞{{sin(1/x)/(1/x)•{1/√[1+sin(1/x)+1]}}=1/2.