# How do you find asymptotic discontinuity?

By setting the denominator equal to zero,

Now, we have a couple of candidates to consider. Let us make sure that there is a vertical asymptote there.

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To find asymptotic discontinuity, you need to analyze the behavior of a function as it approaches a certain value or values.

- Determine the function's domain and any potential points of discontinuity.
- Check if the function approaches different values from the left and right sides of the potential discontinuity point(s).
- If the function approaches different values from the left and right sides, it indicates a potential asymptotic discontinuity.
- Further investigate the behavior of the function by evaluating the limit as it approaches the potential discontinuity point(s) from both sides.
- If the limit does not exist or approaches infinity, the function has an asymptotic discontinuity at that point.
- If the limit exists and approaches a finite value, the function does not have an asymptotic discontinuity at that point.

Remember to consider both one-sided limits and two-sided limits when analyzing asymptotic discontinuity.

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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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