求极限 lim→+0 ∫(√x,0) ((1-cost^2)dt)/(x^(5/2))
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求极限 lim→+0 ∫(√x,0) ((1-cost^2)dt)/(x^(5/2))
求极限 lim→+0 ∫(√x,0) ((1-cost^2)dt)/(x^(5/2))
求极限 lim→+0 ∫(√x,0) ((1-cost^2)dt)/(x^(5/2))
答:
lim(x→0+) [ ∫(√x→0) (1-cost²) dt ] / [ x^(5/2) ] 属于0----0型,可以应用洛必达法则
=lim(x→0+) -(1-cosx)*(1/2√x) / [(5/2)*x^(3/2)]
=lim(x→0+) -2sin²(x/2) / (5x²)
=-2*(x/2)²/(5x²)
=-1/10
看看这个行么?
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