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lim(x^2-1)/(2x^2-x-1)x趋于无穷无穷吗
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lim(x^2-1)/(2x^2-x-1) x趋于无穷 无穷吗
▼优质解答
答案和解析
答案是1/2
lim[x→∞] (x²-1)/(2x²-x-1)
=lim[x→∞] [(x+1)(x-1)]/[(x-1)(2x+1)]
=lim[x→∞] (x+1)/(2x+1)
=lim[x→∞] [(x+1)/x]/[(2x+1)/x]
=lim[x→∞] (1+1/x)/(2+1/x)
=(1+0)/(2+0)
=1/2
lim[x→∞] (x²-1)/(2x²-x-1)
=lim[x→∞] [(x+1)(x-1)]/[(x-1)(2x+1)]
=lim[x→∞] (x+1)/(2x+1)
=lim[x→∞] [(x+1)/x]/[(2x+1)/x]
=lim[x→∞] (1+1/x)/(2+1/x)
=(1+0)/(2+0)
=1/2
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