# What is the limit of #sqrt(9x+x^2)/(x^4+7) # as x approaches infinity?

We have the limit

Factor out the largest-degreed terms from the numerator and denominator of the fraction.

There is also a more intuitive approach to limits of this type.

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The limit of sqrt(9x+x^2)/(x^4+7) as x approaches infinity is 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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