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找出P和Q的值并使得x→∞ 时f(x)=(px^2-2)/(x^2+1)+3qx+5有无穷小

来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/05/22 00:31:52
找出P和Q的值并使得x→∞ 时f(x)=(px^2-2)/(x^2+1)+3qx+5有无穷小

lim(x→∞) (px^2-2)/(x^2+1)+3qx+5 = 0
∴①
0 = lim(x→∞) { (px^2-2)/(x^2+1)+3qx+5 }/x
= lim(x→∞) (px-2/x)/(x^2+1)+3q +5/x
= lim(x→∞) (p/x-2/x^3)/(1+1/x^2) + 3q + 5/x
= 0 + 3q + 0
=3q
∴ q = 0


0 = lim(x→∞) (px^2-2)/(x^2+1) + 5
= lim(x→∞) (p-2/x^2)/(1+1/x^2) + 5
= p + 5
∴ p = -5