作业帮lim (√(x^2+1)+2x)^2/(3x^2+1) x→＋∞
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lim (√(x^2+1)+2x)^2/(3x^2+1) x→＋∞
lim (√(x^2+1)+2x)^2/(3x^2+1) x→＋∞
lim (√(x^2+1)+2x)^2/(3x^2+1) x→＋∞
[√(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
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