这个极限怎么求？
2个回答
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用洛比达法则得
lim<x→+∞>[(100x^99+15x^4)/(x^100+3x^5+1)]/[(20x^19-6)/(x^20-6x+1)]
= lim<x→+∞>(100x^99+15x^4)(x^20-6x+1)/[(x^100+3x^5+1)(20x^19-6)]
(分子分母同除以 x^119)
= lim<x→+∞>(100+15/x^95)(1-6/x^14+1/x^20)/[(1+3/x^95+1/x^100)(20-6/x^19)]
= 100/20 = 5
lim<x→+∞>[(100x^99+15x^4)/(x^100+3x^5+1)]/[(20x^19-6)/(x^20-6x+1)]
= lim<x→+∞>(100x^99+15x^4)(x^20-6x+1)/[(x^100+3x^5+1)(20x^19-6)]
(分子分母同除以 x^119)
= lim<x→+∞>(100+15/x^95)(1-6/x^14+1/x^20)/[(1+3/x^95+1/x^100)(20-6/x^19)]
= 100/20 = 5
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