Give an example of a function with both a removable and a non-removable discontinuity.

Using the continuity concept, it is found that the function with both a removable and a non-removable discontinuity is:

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Continuity:

A function is not continuous at points that are outside it's domain.

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An example can be taken considering a function as follows:

The function is:

A similar example is given at link

Step-by-step explanation:

A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator.  It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x.  In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.

i only know the sequence of arithmetic it adds the first is 5+4 then it goes up as it adds to then it is 9+5 then 14+6 then to 20+7 and so on. 5,9,14,20,27,35.

step-by-step explanation: