已知：lim(x趋向于正无穷)(3x-(ax^2-x+1)^1/2)=b,求常数a,b
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lim(x趋向于正无穷)(3x-(ax^2-x+1)^1/2)=
=lim(x趋向于正无穷)[(3x-(ax^2-x+1)^1/2))(3x+(ax^2-x+1)^1/2)]/(3x-(ax^2-x+1)^1/2)
=lim(x趋向于正无穷)(9x^2-ax^2+x-1)/(3x-(ax^2-x+1)^1/2)
=b
所以9-a=0 a=9
此时 lim(x趋向于正无穷)(x-1)/(3x-(9x^2-x+1)^1/2)
=lim(x趋向于正无穷)(1-1/x)/(3-(9-1/x+1/x^2)^1/2)
=1/(3+√9)=1/6
b=1/6
=lim(x趋向于正无穷)[(3x-(ax^2-x+1)^1/2))(3x+(ax^2-x+1)^1/2)]/(3x-(ax^2-x+1)^1/2)
=lim(x趋向于正无穷)(9x^2-ax^2+x-1)/(3x-(ax^2-x+1)^1/2)
=b
所以9-a=0 a=9
此时 lim(x趋向于正无穷)(x-1)/(3x-(9x^2-x+1)^1/2)
=lim(x趋向于正无穷)(1-1/x)/(3-(9-1/x+1/x^2)^1/2)
=1/(3+√9)=1/6
b=1/6
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