微积分 求极限
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lim(x->1/2) cosπx/(x^2+ax+b) (0/0)
(1/2)^2+a(1/2) +b =0
1+2a+4b =0 (1)
lim(x->1/2) cosπx/(x^2+ax+b) (0/0 分子分母分别求导)
=lim(x->1/2) -π.sinπx/(2x+a)
= -π/(1+a)
=2
-π/(1+a) =2
1+a =-π/2
a= -1-π/2
from (1)
1+2a+4b =0
1+2(-1-π/2)+4b =0
-1 -π +4b=0
b = (1+π)/4
(a,b)=( -1-π/2 , (1+π)/4 )
(1/2)^2+a(1/2) +b =0
1+2a+4b =0 (1)
lim(x->1/2) cosπx/(x^2+ax+b) (0/0 分子分母分别求导)
=lim(x->1/2) -π.sinπx/(2x+a)
= -π/(1+a)
=2
-π/(1+a) =2
1+a =-π/2
a= -1-π/2
from (1)
1+2a+4b =0
1+2(-1-π/2)+4b =0
-1 -π +4b=0
b = (1+π)/4
(a,b)=( -1-π/2 , (1+π)/4 )
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