sin平方=1-cos平方=(1+cos)(1-cos)
分母用三次方公式等于
(1+cos)(1-cos+cos平方)
cosπ=-1
带入
等于2/3
lim(x-> π) (sinx)^2/(1+(cosx)^3)
let
y=π-x
lim(x-> π) (sinx)^2/(1+(cosx)^3)
=lim(y-> 0) (siny)^2/(1-(cosy)^3)
y->0
siny ~ y^2
cosy ~ 1- (1/2)y^3
(cosy)^3 ~[1- (1/2)y^3]^3
~ 1 - (3/2)y^3
1-(cosy)^3 ~ (3/2)y^3
lim(x-> π) (sinx)^2/(1+(cosx)^3)
=lim(y-> 0) (siny)^2/(1-(cosy)^3)
=lim(y-> 0) y^2/[(3/2)y^3]
->∞
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