求极限当X趋近与0时cos(sinx)-cosx/x^4

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根据同阶无穷小，x→0时，闹慎如sinx～x
lim(x→0)cos(sinx)-cosx/x^4
=lim(x→0)cosx-cosx/x^4
=lim(x→0)cosx(1-1/x^4)
=lim(x→0)cosx*lim(x→液启0)(1-1/x^4)
=1*lim(x→孝举0)(1-1/x^4)
=-∞

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=(-2 ( (sin(sinx+x)/2)*(sin(sinx-x)/2))/郑吵x^4
=(-2( (sinx+x)/2)*(sinx-x)/喊闭侍2))/x^4
=(-2( (sinx+x)/态汪2)/x*(sinx-x)/2)/x^3)
=1/6

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