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](/uploads/image/z/16864617-57-7.jpg?t=lim+%28x%E2%86%920%29%28%E2%88%AB%28%E4%B8%8Ax%E4%B8%8B0%29%281-cost%29dt%29%2Fx%5E3)
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.
=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.
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