lim x趋向0 [x(1-cos2x)]/(5x-sin5x)?知道答案是12/125,

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lim x趋向0 [x(1-cos2x)]/(5x-sin5x)?知道答案是12/125,
lim x趋向0 [x(1-cos2x)]/(5x-sin5x)?
知道答案是12/125,

lim x趋向0 [x(1-cos2x)]/(5x-sin5x)?知道答案是12/125,
lim x趋向0 [x(1-cos2x)]/(5x-sin5x)＝lim x趋向0 [x2(sinx)^2]/(5x-sin5x)=lim x趋向0 [2x^3]/(5x-sin5x)=lim x趋向0 [6x^2]/(5-5cos5x)＝lim x趋向0 [12x]/(25sin5x)＝lim x趋向0 [12]/(125cos5x)＝lim x趋向0 12/125=12/125

x趋于0
1-cosx~x²/2
所以1-cos2x~(2x)²/2=2x²
sinx=x-x³/3!+o(x³)
sin5x=5x-(5x)³/3!+o(x³)
所以原式=limx*2x²/[5x-5x+(5x)³/3!+o(x³)]
=lim2x&...

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x趋于0
1-cosx~x²/2
所以1-cos2x~(2x)²/2=2x²
sinx=x-x³/3!+o(x³)
sin5x=5x-(5x)³/3!+o(x³)
所以原式=limx*2x²/[5x-5x+(5x)³/3!+o(x³)]
=lim2x³/[(5x)³/6+o(x³)]
=12/125

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