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

What are the removable and non-removable discontinuities, if any, of #f(x)=(x^2 +10x+ 24) /( x+6) #?

Answer 1

Scarlett Allison

There is a removable discontinuity at #-6#

#f(-6)# does not exist, so #f# is not continuous at #-6#, but

#lim_(xrarr-6)(x^2+10x+24)/(x+6) = lim_(xrarr-6) (x+4) = -2#

so the discontinuity is removable.

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Answer 2

Charles Anctil

The removable discontinuity of f(x) is at x = -6. 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.