求lim x→(兀/2) (tanx/tan3x)
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lim(x->π/2) (tanx/tan3x) (∞/∞)
=lim(x->π/2) (secx)^2/[ 3(sec3x)^2]
=lim(x->π/2) (cos3x)^2/[ 3(cosx)^2 ] (0/0)
=lim(x->π/2) -3sin6x/( -3sin2x)
=lim(x->π/2) sin6x/sin2x (0/0)
=lim(x->π/2) 6cos6x/(2cos2x)
=-6/(-2)
=3
=lim(x->π/2) (secx)^2/[ 3(sec3x)^2]
=lim(x->π/2) (cos3x)^2/[ 3(cosx)^2 ] (0/0)
=lim(x->π/2) -3sin6x/( -3sin2x)
=lim(x->π/2) sin6x/sin2x (0/0)
=lim(x->π/2) 6cos6x/(2cos2x)
=-6/(-2)
=3
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