Home > Calculus > Classifying Topics of Discontinuity (removable vs. non-removable)

What are the removable and non-removable discontinuities, if any, of #f(x)=(x^4 - 1)/(x-1) #?

Answer 1

Removable discontinuity at #x =1#

In a fractional function, discontinuities are caused by the denominator. We know that the denominator CANNOT be equal to 0.

Hence, #x - 1# cannot be equal to 0 In other words, x cannot be equal to 1, which is the value of x at which the function presents a discontinuity.

Since, there's only 1 value of x for which the function is not defined, it is a removable discontinuity.

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Answer 2

Isabella Ackerman

The removable discontinuity of f(x) = (x^4 - 1)/(x-1) is at x = 1. There are no non-removable discontinuities.

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Answer from HIX Tutor

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.