⑩天掌 Teaching Plan on Advanced Mathematics arcsin x 例13求lm x→0 解令t=sinx,则x=sin,当x→Q时,有t→>0 于是由复合函数的极算法则得 arcsin m x→>0 x→0smnt 2.单调有界准则 如果数列x满足条件 x1≤x2…≤xn≤xn1≤…,单调增加 单调数列 x1≥x2…≥xn≥xn+1≥…,单调减少 准则Ⅱ单调有界数列必有极限Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 例13 求 x x x arcsin lim →0 解 于是由复合函数的极限运算法则得 令t = sin x,则x = sint,当x → 0时,有t → 0. 1 sin lim arcsin lim 0 0 = = → → t t x x x x 2.单调有界准则 如果数列x n满足条件 , x1  x2  xn  xn+1   单调增加 , x1  x2  xn  xn+1   单调数列 单调减少 准则Ⅱ 单调有界数列必有极限