lim(x趋于∞)(x^2-5x+1/x^2-2x+3)^2x+1次幂的极限怎么求
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lim(x -> ∞)(x^2-5x+1/x^2-2x+3)^(2x+1)
= lim(x -> ∞)e^ (2x+1)ln(x^2-5x+1/x^2-2x+3)
= lim(x -> ∞)e^ [(2x+1)((x^2-5x+1/x^2-2x+3) - 1)] (Taylor expansion: ln x ~ x - 1
= lim(x -> ∞)e^[(2x+1)(-3x)/(x^2)] (after ignoring lower degree terms)
= e^(-6)
= lim(x -> ∞)e^ (2x+1)ln(x^2-5x+1/x^2-2x+3)
= lim(x -> ∞)e^ [(2x+1)((x^2-5x+1/x^2-2x+3) - 1)] (Taylor expansion: ln x ~ x - 1
= lim(x -> ∞)e^[(2x+1)(-3x)/(x^2)] (after ignoring lower degree terms)
= e^(-6)
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