limx→0(cosx)^(1/x^2)求解
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limx→0(cosx)^(1/x^2)求解
lim(x→0)((cosx)^(1/x^2))
lim(x→0)((cosx)^(1/x^2))
![limx→0(cosx)^(1/x^2)求解](/uploads/image/z/16743368-56-8.jpg?t=limx%E2%86%920%28cosx%29%5E%281%2Fx%5E2%29%E6%B1%82%E8%A7%A3)
lim(x→0)((cosx)^(1/x^2))
=lim(x→0)[1-2sin^2(x/2)]^(1/x^2))
=lim(x→0){[1-2sin^2(x/2)]^(-1/[2(x/2)^2)]}^(-1/2)
=lim(x→0){[1-2sin^2(x/2)]^(-1/[2sin)^2(x/2)]}^(-1/2)
=e^(-1/2)
=lim(x→0)[1-2sin^2(x/2)]^(1/x^2))
=lim(x→0){[1-2sin^2(x/2)]^(-1/[2(x/2)^2)]}^(-1/2)
=lim(x→0){[1-2sin^2(x/2)]^(-1/[2sin)^2(x/2)]}^(-1/2)
=e^(-1/2)
还有一道 limx→0 (1-cosx)/x^2
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