How do you find the limit of x/(sqrt(4x^2 - x + 3)) as x approaches negative infinity?

1 Answer
Konstantinos Michailidis
Mar 12, 2016

It is

lim_(x->-oo) x/(sqrt(4x^2 - x + 3))= lim_(x->-oo) x/[absx*sqrt[4-1/x+3/x^2]]= lim_(x->-oo) x/[(-x)*sqrt[4-1/x+3/x^2]]= lim_(x->-oo) -1/[sqrt[4-1/x+3/x^2]]= lim_(x->-oo) -1/[sqrt(4-0+0)]= =-1/2

Note that as x->-oo , absx=-x and 1/x->0 , 1/x^2->0

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