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lim{[根号(x^2+1)]+2X}^2/(3x^2+1)
题目详情
lim{[根号(x^2+1)]+2X}^2/(3x^2+1)
▼优质解答
答案和解析
[√(x^2+1)+2x]^2/(3x^2+1)
=[|x|√(1+1/x^2)+2x]^2/x^2(3+1/x^2)
=x^2[√(1+1/x^2)+2]^2/x^2(3+1/x^2) 注意这里|x|^2=x^2,所以x可以提出来.
=[√(1+1/x^2)+2]^2/(3+1/x^2)
所以 limx->∞{[√(1+1/x^2)+2]^2/(3+1/x^2)}
=(√1+2)^2/3
=9/3=3
=[|x|√(1+1/x^2)+2x]^2/x^2(3+1/x^2)
=x^2[√(1+1/x^2)+2]^2/x^2(3+1/x^2) 注意这里|x|^2=x^2,所以x可以提出来.
=[√(1+1/x^2)+2]^2/(3+1/x^2)
所以 limx->∞{[√(1+1/x^2)+2]^2/(3+1/x^2)}
=(√1+2)^2/3
=9/3=3
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