求一个极限:x取向无穷,(sin(2/x)+cos(1/x))^x
问题描述：
求一个极限:x取向无穷,(sin(2/x)+cos(1/x))^x
答
原式=lim(y->0)[(sin(2y)+cosy)^(1/y)] (令y=1/x)=lim(y->0)[(1+(sin(2y)+cosy-1))^(1/y)]=lim(y->0){[(1+(sin(2y)+cosy-1))^(1/(sin(2y)+cosy-1))]^[(sin(2y)+cosy-1)/y]}={lim(y->0)[(1+(sin(2y)+cosy-1))^(1/(sin...