# How do you find the limit of #| x - 5 |# as x approaches #5#?

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If you are doing this to prove that the function is continuous, rewrite using the definition of absolute value.

So,

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To find the limit of | x - 5 | as x approaches 5, we can evaluate the expression for values of x that approach 5 from both the left and right sides.

When x approaches 5 from the left side (x < 5), the expression simplifies to -(x - 5), which is equal to 5 - x.

When x approaches 5 from the right side (x > 5), the expression simplifies to x - 5.

Since the limit from both sides is the same, the limit of | x - 5 | as x approaches 5 is equal to 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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