tan 5x-cosx+1 王例5求 sin 3x H tanx=5x+o(x), sin 3x=3x +o(x), 1-c0sx=x2+0(x2) 2 5x+0(x)+x2+o(x 原式=lim 2 →0 3x+0(x) —+,xx2) 0(x 5+ 5 3+(x) 3 上页例 5 . sin 3 tan 5 cos 1 lim0 x x x x − + → 求 解 tan x = 5 x + o(x), sin 3x = 3x + o(x), ( ). 21 1 cos 2 2 − x = x + o x3 ( ) ( ) 21 5 ( ) lim 2 2 0 x o x x o x x o x x + + + + = → 原式 x o x x o x x x o x x ( ) 3 ( ) 2 ( ) 1 5 lim 2 0 + + + + = → . 35 =