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求极限,能否不用洛必达法则
2个回答
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可以
令t=2x+π/3,则当t→π/3时x→0
分子=π-3(2x+π/3)=-6x
分母=cos(2x+π/3)-cos(π/3)=-2sin(x+π/3)sinx
等价替换sinx~x,化简得原式=lim(x→0)3/sin(x+π/3)=3/(√3/2)=2√3
令t=2x+π/3,则当t→π/3时x→0
分子=π-3(2x+π/3)=-6x
分母=cos(2x+π/3)-cos(π/3)=-2sin(x+π/3)sinx
等价替换sinx~x,化简得原式=lim(x→0)3/sin(x+π/3)=3/(√3/2)=2√3
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