# How do you find the limit of #abs(x-4) / (x-4)# x as it approaches 4 from the left and right?

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The limit of abs(x-4) / (x-4) as x approaches 4 from the left is -1, and as x approaches 4 from the right, it 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.

- How do you find the limit of #(sin^4x)/(x^(1/2))# as x approaches infinity?
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- How do you find the limit of # (1 - x + log_ex) / (1 - sqrt(2x - x^2))# as x approaches 1?

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