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洛必达求极限lim(x→2/Π) tAnx/tAn3x 答案已给出

: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

答案

lim (1/x² - cot²x),x趋向0 = lim (1/x² - cos²x/sin²x),通分 = lim (sin²x - x²cos²x)/(x²sin²x),分母sin²x等价x² = lim cos²x(tan²x - x²)/x^4,分子提取cos&...

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