Question

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

Answer 1

Could you help? @satellite73

Answer 2

sure

Answer 3

removable discontinuity is one of those "factor and cancel" deals, like for example
\[\frac{x^2-4}{x-2}\] this is undefined at \(x=2\) but it is also true that if \(x\neq 2\) this is the same as
\[\frac{(x+2)(x-2)}{x-2}=x+2\]

Answer 4

the discontinuity is "removable" because... well because when you factor and cancel you remove it

Answer 5

and so the non-removable discontinuity would be x+2 ?

Answer 6

because it isn't removed?

Answer 7

lol no
that is not a discontinuity
that is an expression

Answer 8

so the discontinuity is the entire thing? where parts cancel each other out?

Answer 9

the discontinuity was at \(2\) and we removed it when we rewrote \[\frac{(x+2)(x-2)}{x-2}=x+2\]

Answer 10

the discontinuity is at a number
\(2\) was the removable discontinuity

Answer 11

and what does 2 represent?

Answer 12

Are you there? @satellite73