# How do you evaluate the limit #sqrt(x-2)-sqrtx# as x approaches #oo#?

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expanding by Binomial Expansion

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We can rewrite this square root using its conjugate:

We can try to take a factor from the denominator:

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The limit of sqrt(x-2)-sqrtx as x approaches infinity is -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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