# How do you find the x values at which #f(x)=abs(x-3)/(x-3)# is not continuous, which of the discontinuities are removable?

Refer to the Discussion given in the Explanation Section below.

continuous at that point.

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Then we analyze separately:

The discontinuity cannot be removed, as clearly:

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The function f(x) = abs(x-3)/(x-3) is not continuous at x = 3. This is because the denominator becomes zero at x = 3, which results in an undefined value for the function.

The discontinuity at x = 3 is removable. This means that if we redefine the function at x = 3, we can make it continuous. By simplifying the expression, we can rewrite f(x) as 1 for all x ≠ 3. Therefore, we can redefine f(3) = 1 to make the function continuous at x = 3.

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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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