lim(x→∞) ((3x^2+1)^(1/2)-(3x^2-x)^(1/2))

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lim(x→∞) ((3x^2+1)^(1/2)-(3x^2-x)^(1/2))

lim(x→∞) ((3x^2+1)^(1/2)-(3x^2-x)^(1/2))
lim(x→∞) ((3x^2+1)^(1/2)-(3x^2-x)^(1/2))

lim(x→∞) ((3x^2+1)^(1/2)-(3x^2-x)^(1/2))

lim(x→∞) ((3x^2+1)^(1/2)-(3x^2-x)^(1/2))
=lim((3x^2+1)^(1/2)-(3x^2-x)^(1/2))*((3x^2+1)^(1/2)+(3x^2-x)^(1/2))/((3x^2+1)^(1/2)+(3x^2-x)^(1/2))
=lim(1+x)/((3x^2+1)^(1/2)+(3x^2-x)^(1/2))
=lim(x/(2*√3x)
=√3/6

6分之根号3

lim(x→∞) ((3x^2+1)^(1/2)-(3x^2-x)^(1/2))=lim(x->∞)(1+x)/[(3x^2+1)^(1/2)+(3x^2-x)^(1/2)]
=lim(x->∞)(1+1/x)/[(3+1/x^2)^(1/2)+(3-1/x)^(1/2)]
=1/2√3

原式=lim(x趋近于无穷大)[x根号(3+1/x^2)--x根号(3--1/x)]
=x(根号3)--x(根号3)
=0.

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