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tAnx%sinx

tanx=y/x (tanx)^2=y^2/x^2 1/(tanx)^2=x^2/y^2 1/(tanx)^2+1=1+x^2/y^2=(x^2+y^2)/y^2=r^2/y^2=(1/sinx)^2 ∴1/【1/(tanx)^2+1】=(sinx)^2 sinx=√{1/【1/(tanx)^2+1】}

lim(x→0)(tanx-sinx)/(sinx)^3 =lim(x→0)tanx(1-cosx)/x^3 =lim(x→0)x*(1/2x^2)/x^3 =1/2

(sinx-cosx)/(1-tanx)=(sinx-cosx)/(1-sinx/cosx)=cosx(sinx-cosx)/(cosx-sinx)=-cosx.

sin0=0、sin(π/6)=1/2、sin(π/4)=(√2)/2、sin(π/3)=(√3)/2、sin(π/2)=1; cos0=1、cos(π/6)=(√3)/2、cos(π/4)=(√2)/2、cos(π/3)=1/2、cos(π/2)=0; tan0=0、tan(π/6)=(√3)/3、tan(π/4)=1、tan(π/3)=√3、tan(π/2)=+∞; 然后,由诱导公式及周期性...

tan(tanx) tan(sinx) =tan(tanx +sinx)*(1-tanxsinx )

对。(但是是在X为锐角时) sinX=a/c cosX=b/c sinX/cosX=(a/c)/(b/c)=a/b=tanX

lim(tanx-sinx/sin³x)=lim(1-cosx)/sin²x=lim 2sin²(x/2)/sin²x=(x²/2)/x²=1/2 x→0

见图。

解: tanx+sinx

lim(tanx-sinx)/sin³x =lim(sinx/cosx -sinx)/sin³x =lim(1/cosx -1)/sin²x =lim(1-cosx)/[cosx·(1-cos²x)] =lim(1-cosx)/[cosx·(1+cosx)(1-cosx)] =lim1/[cosx(1+cosx)] =1/[1×(1+1)] =1/2 本题非常简单,连等价无穷小都没...

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