# How can you remove a discontinuity?

Please see below.

Example

So we remove the discontinuity by defining:

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To remove a discontinuity in a function, you can use a process called "removable discontinuity removal" or "remediation." This involves finding the limit of the function as it approaches the point of discontinuity and then redefining the function at that point to make it continuous. This can be done by either algebraically simplifying the function or by introducing a new term that cancels out the 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.

- What is the limit of #xe^(1/x) - x# as x approaches infinity?
- How do you find the limit of #cos(3x)# as #x->pi#?
- For what values of x, if any, does #f(x) = tan((-7pi)/4-2x) # have vertical asymptotes?
- How do you find the limit of #ln(t)^2/ (t)# as t approaches infinity?
- How do you find the limit of #((sqrtx+4)-3)/(x-6)# as x approaches 6?

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