极限lim(x->∞)(ax^2+x+1)/(2x^2+x-5)=3,则a=_______(求详细过程!)

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极限lim(x->∞)(ax^2+x+1)/(2x^2+x-5)=3,则a=_______(求详细过程!)
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极限lim(x->∞)(ax^2+x+1)/(2x^2+x-5)=3,则a=_______(求详细过程!)
极限lim(x->∞)(ax^2+x+1)/(2x^2+x-5)=3,则a=_______(求详细过程!)

极限lim(x->∞)(ax^2+x+1)/(2x^2+x-5)=3,则a=_______(求详细过程!)
∵lim(x->∞)[(ax^2+x+1)/(2x^2+x-5)]=3
==>lim(x->∞)[(a+1/x+1/x^2)/(2+1/x-5/x^2)]=3
==>(a+0+0)/(2+0-0)=3
==>a/2=3
∴a=6.