# What is the limit of #(-2x+1)/sqrt(x^2 +x)# as x goes to infinity?

Here is the graph, so we can see the two horizontal asymptotes.

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graph{(-2x+1)/sqrt(x^2 +x) [-25.9, 31.81, -14.4, 14.46]}

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The limit of (-2x+1)/sqrt(x^2 +x) as x goes to infinity is -2.

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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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