# How do you evaluate # ( x^2+2) /( sqrt (9x^4 +1))# as x approaches infinity?

Rewrite using algebra so that the limit does not have indeterminate form.

And

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As x approaches infinity, the expression (x^2+2)/(sqrt(9x^4+1)) can be evaluated by considering the highest power of x in the numerator and denominator. In this case, the highest power of x is x^4.

Dividing both the numerator and denominator by x^4, we get (1/x^2 + 2/x^4) / (sqrt(9 + 1/x^4)).

As x approaches infinity, 1/x^2 and 2/x^4 both approach 0, and 1/x^4 approaches 0 as well.

Therefore, the expression simplifies to 0 / sqrt(9) = 0.

So, as x approaches infinity, (x^2+2)/(sqrt(9x^4+1)) approaches 0.

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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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