limit x=pi/2 cosx/(x-pi/2)

2012-10-22 11:35 am

limit x=pi/2 cosx/(x-pi/2) =-1
請問步驟係點

回答 (3)

2012-10-22 1:36 pm

✔ 最佳答案

lim(x->π/2)_Cosx/(x－π/2)=－1
請問步驟係點
Sol
lim(x->π/2)_Cosx/(x－π/2) 0/0 type
=lim(x->π/2)_－sinx/1
=－1

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2012-10-22 7:03 pm

cosx = sin(pi/2 -x ) = - sin( x- pi/2)

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2012-10-22 5:45 pm

【設y=x - π/2，x = y +π/2 ，x->π/2 時 y->0】

lim[x->π/2] cos x/(x - π/2)
= lim[y->0] cos (y+π/2) / y
=lim[y->0] (- sin y) / y
= -1*1 = -1

或使用洛必達法則如一號回答所示

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