lim(x→1)[(cos(π/2)x]/(1-x)
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lim(x→1)[(cos(π/2)x]/(1-x)
lim(x→1)[(cos(π/2)x]/(1-x)
lim(x→1)[(cos(π/2)x]/(1-x)
lim(x→1)[(cos(π/2)x]/(1-x)
=
lim(x→1)[(-π/2sin(π/2)x]/(-1)
=π/2
lim(x-->1) cos(πx/2)/(1 - x)
= lim(x-->1) sin(π/2 - πx/2)/(1 - x) <== cosθ = sin(π/2 - θ)
= lim(x-->1) sin(π/2 - πx/2)/(π/2 - πx/2) * (π/2 - πx/2)/(1 - x)
= lim(x-->1) sin(π/2 - πx/2)/(π/2...
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lim(x-->1) cos(πx/2)/(1 - x)
= lim(x-->1) sin(π/2 - πx/2)/(1 - x) <== cosθ = sin(π/2 - θ)
= lim(x-->1) sin(π/2 - πx/2)/(π/2 - πx/2) * (π/2 - πx/2)/(1 - x)
= lim(x-->1) sin(π/2 - πx/2)/(π/2 - πx/2) * (π/2)(1 - x)/(1 - x)
= (1)(π/2)(1),最前面一项是重要公式:lim(x-->0) (sinx)/x = 1
= π/2
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