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)/(x^2-3x-10)#?

Answer 1

Aurora Alvarado

Removable discontinuity at #x=-2#.
Non-removable discontinuity at #x=5#.

After factorization,

#f(x)=frac{x+2}{x^2-3x-10}#

#=frac{x+2}{(x+2)(x-5)}#

#lim_{x->-2}f(x)=-1/7#

#lim_{x->5}f(x)# is undefined.

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Answer 2

Ezekiel Alexander

The removable discontinuity of f(x) = (x+2)/(x^2-3x-10) occurs at x = -2. 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.