How do you find the limit of #(x^5+3)/(x^2+4)# as #x->oo#?

Answer 1

#oo#

#(x^5+3)/(x^2+4)#
Divide by #x^2#
#(x^5/x^2+3/x^2)/(x^2/x^2+4/x^2)=(x^3/1+3/x^2)/(1+4/x^2)#
as #x->oo# , #(x^3/1+3/x^2)/(1+4/x^2)=(oo+0)/(1+0)->oo#
#:.#
#lim_(x->oo)((x^5+3)/(x^2+4))=oo#
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Answer 2

To find the limit of (x^5+3)/(x^2+4) as x approaches infinity, we can divide both the numerator and denominator by the highest power of x, which is x^5. This gives us (1 + 3/x^5)/(1/x^3 + 4/x^5). As x approaches infinity, 3/x^5 and 4/x^5 both approach zero. Therefore, the limit simplifies to 1/0, which is undefined.

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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.

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.

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.

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.

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