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lim x→0 1%Cos4x/xsinx=

(x→0) lim (1-cos4x)/(xsinx) = (x→0) lim 2sin²(2x)/(xsinx) = (x→0) lim 2sin(2x)*2sinxcosx/(xsinx) = (x→0) lim 4sin(2x)*cosx/x = (x→0) lim 8cosx *sin(2x)/(2x) = 8*cos0*1 = 8

(x→0) lim (1-cos4x)/(xsinx) = (x→0) lim 2sin²(2x)/(xsinx) = (x→0) lim 2sin(2x)*2sinxcosx/(xsinx) = (x→0) lim 4sin(2x)*cosx/x = (x→0) lim 8cosx *sin(2x)/(2x) = 8*cos0*1 = 8

等价无穷小 1-cos4x~1/2*(4x)^2=8x^2 xsinx~x^2 原式=8

∫ 1/(sinxcos⁴x) dx = ∫ cscxsec⁴x dx = ∫ cscx(1 + tan²x)² dx = ∫ cscx(1 + 2tan²x + tan⁴x) dx = ∫ (cscx + 2secxtanx + secxtan³x) dx = ∫ cscx dx + 2∫ secxtanx dx + ∫ secxtanx(sec²x - 1) d...

x→0时 原式=lim(x→0)(-sinx+4sin4x)/2x =lim(x→0)(-cosx+16cos4x)/2 =(-1+16)/2 =15/2

lim(x->0)1/(sinx^2)-1/(x^2cosx^2) =lim(x->0)4[(x^2+1)cosx^2-1)/[xsin2x]^2 =lim(x->0)4* (2xcosx^2-(x^2+1)sin2x)/[2xsin2x*(sin2x+2xcos2x)] =lim(x->0)4*[2cosx^2-8xsin2x-4x^2cos2x-2cos2x)]/[2(sin2x)^2+2xsin4x+2xsin4x+x^2cos4x] =lim...

(Ⅰ) f(x)=(cos4x-sin4x)-2sinx?cosx=(cos2x-sin2x)-sin2x=cos2x-sin2x=2cos(2x+π4). …(4分)∴f(x)的最小正周期T=2π2=π. …(6分)(Ⅱ)令2kπ≤2x+π4≤2kπ+π,…(8分)则kπ-π8≤x≤kπ+3π8,k∈Z.故f(x)的单调递减区间为[kπ-π8,kπ+3π...

y=cos⁴x y'=-4sinxcos³x

(1)∵y=sin4x+23sinxcosx?cos4x+1==(sin2x+cos2x)(sin2x?cos2x)+3sin2x+1=3sin2x?cos2x+1 =2sin(2x?π6)+1.…(4分)所以,该函数的最小正周期 T=2π2=π. …(6分)令2x?π6=kπ,则x=k2π+π12,所以对称中心为(k2π+π12,1),k∈Z.…(8分)(2...

左边=(sinx cosx)分之(sin5xcosx-cos5xsinx) =(2分之1倍sin2x)分之sin4x =sin2x分之2sin4x =sin2x分之4sin2xcos2x =4cos2x 原方程等价于:4cos2x=2 即:cos2x=2分之1 2x=2kπ±3分之π x=kπ±6分之π

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