Question

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

Answer 1

There is a removable discontinuity at `-6`

Explanation:

`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.