求limx→∞x{√[1+sin(1/x)-1]}

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