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lim(tan(tanx)-sin(sinx))/x^3         (x~0)

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sxooo18997

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ÒýÓûØÌû:
2Â¥: Originally posted by Edstrayer at 2014-04-09 09:50:21
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3Â¥2014-04-09 14:01:10
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zywang1999

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sinx = x - x^3/3! + o(x^3)
sin(sinx) = sinx - (sinx)^3/6 + o(x^3)
=x - x^3/6 - x^3/6+ o(x^3)
=x - x^3/3+ o(x^3)
tanx = x + x^3/3 + o(x^3)
tan(tanx) =tanx + (tanx)^3/3 + o[(tanx)^3]
= x + x^3/3 + x^3/3 + o[x^3]
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4Â¥2014-04-09 15:52:09
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sxooo18997

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ÒýÓûØÌû:
4Â¥: Originally posted by zywang1999 at 2014-04-09 15:52:09
xÇ÷ÓÚ0ʱ£¬
sinx = x - x^3/3! + o(x^3)
sin(sinx) = sinx - (sinx)^3/6 + o(x^3)
=x - x^3/6 - x^3/6+ o(x^3)
=x - x^3/3+ o(x^3)
tanx = x + x^3/3 + o(x^3)
tan(tanx) =tanx + (tanx)^3/3 + o
= x + x^3/ ...

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5Â¥2014-04-09 20:52:25
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