# Does the function # f(x) = x/(|x|-3)# have any discontinuities?

There are discontinuities when

We have:

ie there could only be a discontinuity if

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Yes, the function f(x) = x/(|x|-3) has a discontinuity at x = 3.

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Yes, the function ( f(x) = \frac{x}{|x|-3} ) has a discontinuity at ( x = 3 ) because the denominator becomes zero at that point, which results in division by zero, making the function undefined. Hence, ( x = 3 ) is a point of discontinuity for this function.

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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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