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

Answer 1

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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Answer 2

Christopher Agresta

To find the limit of x/(sqrt(4x^2 - x + 3)) as x approaches negative infinity, we can simplify the expression by dividing both the numerator and denominator by x. This gives us 1/(sqrt(4 - 1/x + 3/x^2)). As x approaches negative infinity, both 1/x and 3/x^2 approach 0. Therefore, the expression simplifies to 1/(sqrt(4)) = 1/2. Thus, the limit of x/(sqrt(4x^2 - x + 3)) as x approaches negative infinity is 1/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.