例4设x>0,且Imxn=a>0, n→0 求证lim/xn=√ n→0 证任给E>0, lim x=,(对1=√E) 丑N使得当n>N时恒有xn-a<E1 从而有xn-a=2-a:-aE .+va n 故im√xn=√a例 4 lim . 0, lim 0, x a x x a n n n n n =  =  → → 求证设 且 证 任给  0 , lim x a, n n = →   , 1 N n  N x − a   使得当 时恒有 n x a x a x a nn n +− 从而有 − = a x a n −  a1   =  lim x a. n n = →  故 ( ) 1 对  = a