# How do you find the limit #sqrt(x^2+x)-sqrt(x^2-x)# as #x->oo#?

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

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To find the limit of (\sqrt{x^2 + x} - \sqrt{x^2 - x}) as (x) approaches infinity ((x \rightarrow \infty)), you can use algebraic manipulation and limit properties. After simplification, the limit evaluates to (1).

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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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