sinx+cosx-1/sin3x-x2(平方)求极限x趋向0

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sinx+cosx-1/sin3x-x2(平方)求极限x趋向0sinx+cosx-1/sin3x-x2(平方)求极限x趋向0sinx+cosx-1/sin3x-x2(平方)求极限x趋向0(x→0)li

sinx+cosx-1/sin3x-x2(平方)求极限x趋向0
sinx+cosx-1/sin3x-x2(平方)求极限x趋向0

sinx+cosx-1/sin3x-x2(平方)求极限x趋向0
(x→0) lim (sinx+cosx-1)/(sin3x-x^2)
= (x→0) lim [sinx - 2 sin^2(x/2)] / (sin3x-x^2)
= (x→0) lim [(sinx)/x- sin^2(0.5x)/(0.5x)] / [3(sin3x)/3x - x] 上下同除以 x,利用重要极限(sinx)/x
= (x→0) lim [1-sin(0.5x)] / (3*1-x)
=1/3