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换元法 ∫sinxCosx/(1+sin^4x) Dx

∫sinxcosx/(1+sin^4x)dx =∫sinx/(1+sin^4x)d(sinx) =1/2*∫1/(1+(sin^2x)^2)d(sin^2x) =1/2*arctan(sin^2x)+C

数学题求解 del1回答如图,正方形ABCD的边长为4,正方形ECFG的边长为8,求阴影部分的面积...del2回答若x平方等于2,则x等于del2回答高二数学数学,在线求助。del0回答15求解a[a(a+b)]b=1,求a+b=?del0回答9/10Y+3/8y=3/4 9/10Y+3/8y=3/4 9/10Y+3/8...

因为:cos4x+sin4x+sin2xcos2xsin6x+cos6x+2sin2xcos2x=(sin 2x+cos 2x) 2?2sin 2xcos 2x +sin 2xcos 2x (sin 2x+cos 2x) [(sin 2x) 2?sin 2xcos 2x+(cos 2x ) 2]+ 2sin 2xcos 2x =1?sin 2xcos 2x (sin 2x) 2+(cos 2x) 2+sin 2xcos 2x =1?sin 2x...

函数f(X)=ba=COS^4x-SIN^4x-3^-2COSx2sinx =COS^2x-SIN^2x-3^-2COSx2sinx =cos2x-3^-2sin2x =4根号下7/9 cos(2x+a) a=arc sins根号下7/28 90度<2x+a <180度,解出即可

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∵当x→0时,ln(1+sin4x)~sin4x~x41-cosx~12x2又sinxcosxcos2x=12sin2xcos2x=14sin4x∴limx→0f(x)g(x)=limx→0x?14sin4xln(1+sin4x)?x=limx→0x?14sin4xx3=limx→01?cos4x3x2=limx→0?16x223x2=?83∴f(x)是g(x)的同阶但非等价无穷小故选:C.

因为f(x)=cos4x-2sinxcosx-sin4x=(sin2x+cos2)(cos2-sin2x)-sin2x=cos2x-sin2x=2cos(2x+π4),所以当cos(2x+π4)=1时,函数的最大值为2;故选C.

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