lim (x→0)(∫(上x下0)(1-cost)dt)/x^3

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lim (x→0)(∫(上x下0)(1-cost)dt)/x^3
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lim (x→0)(∫(上x下0)(1-cost)dt)/x^3
lim (x→0)(∫(上x下0)(1-cost)dt)/x^3

lim (x→0)(∫(上x下0)(1-cost)dt)/x^3
原式=lim(x->0)[(x-sinx)/x^3]
=lim(x->0)[(1-cosx)/(3x^2)] (0/0型极限,应用罗比达法则)
=lim(x->0)[sinx/(6x)] (0/0型极限,应用罗比达法则)
=(1/6)lim(x->0)(sinx/x)
=(1/6)*1 (应用重要极限)
=1/6.