Question

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

Answer 1

well, what makes a discontinuity removable?

Answer 2

It's one that can be fixed to create a straight line. While non-removable means it cannot be fixed.

Answer 3

well, mathically ... i would say that a removable discontinuity can be canceled top to bottom ... k/k = 1 after all, and 1*a = a

Answer 4

My teacher explained it by using common everyday examples and that's the only way I remembered it lol.

Answer 5

so, lets for a removable setup:\[\frac{(x-r)}{(x-r)}\]
something that cant be removed has no common factor to cancel it out sooo\[\frac{(x-r)}{(x-r)(x-c)}\]has both a removable and a non removable discontiuity ...

Answer 6

So for removable would be like \[\frac{ x-5 }{ x+5 }\] or would it be two different numbers?

Answer 7

does (x-5) cancel out (x+5) ?

Answer 8

Oh okay. So it has to cancel out.

Answer 9

lets chk ... say x=3
\[\frac{ 3-5 }{ 3+5 }=\frac{-2}{8}\ne1\]they dont cancel

Answer 10

yeah, to remove it, you need to be able to 'remove' it .... to 'cancel' it out

Answer 11

Thanks for the explanations. Really helped!

Answer 12

good luck :)

Answer 13

Thanks!