x->0 2 推论 COS x lim x>01 October 2004
October, 2004 2 0 1 cos 1 lim x 2 x → x − = 0 2 1 cos lim 1 2 x x x → − = 1 推论
2 X lin =11-cosx≈-(x->0) x->0 2 2 2 0.5 ith (plots): M:=5 A:=plot(1-cos(x),x=-M..M,y=-.51.3) October 2004
October, 2004 with(plots):M:=5: A:=plot(1 -cos(x),x= -M..M,y= -.51..3): B:=plot(x^2/2,x= -M..M,y= -.51..3,color=blue): display(A,B,scaling=constrained,thickness=3); 2 1 cos ( 0 2 ) x − x →x 0 2 1 cos lim 1 12 x x x → − =
例求 lim x sin x→0 解 Esin (∞.0型)或令 x→>00 X X x→>∞<t→>0 SIn = lim x-→>∞1 型) 0 limx sin x→>0 X lim sin t t-0 October 2004
October, 2004 例 求 1 lim sin x x → x 解 1 lim sin x x → x ( 0 ) 型 1 sin limx 1 x x → = 0 ( ) 0 型 = 1 或令 1 t x = x → t →0 0 sin lim t t → t = 1 lim sin x x → x = 1
limx -=1 x→0 05 .5 with(plots): M: =2 :=p1ot(x*sin(1/x),x=-M.,M,y=-1.5..1 ctober 2004
October, 2004 with(plots):M:=2: A:=plot(x*sin(1/x),x= -M..M,y= -1.5..1.5): B:=plot(1,x= -M..M,y= -1.5..1.5,color=blue): 1 lim sin 1 x x → x =