Question

find the x values (if any) at which f is not
continuous. Which of the discontinuities are removable? f(x)=x-3/x^2-9

Answer 1

I got an answer, then my teacher said it was wrong.... She said you created a hole in the graph at x=3 which is a removable discontinuity. A non-removable discontinuity happens when the denominator =0 (after you factored and reduced). HELP?

Answer 2

@ParthKohli @Calcmathlete @Hero

Answer 3

well the question asks where are the removable discontinuities... You said at x=3, which is correct. Is there another part to the question?

Answer 4

Also, do you understand why it's removable?

Answer 5

I know that x=3 creates a hole, so that is removable discontinuity. Idk the rest..

Answer 6

No the only question is the one written above^^

Answer 7

It's not that it's because it creates a hole. There's another reason why. Can you factor x^2-9 to be in the form, (x - )(x + ) ?

Answer 8

(x-3)(x+3). then it leaves you with just 1/x+3

Answer 9

So the reason why x=3 is a removable discontinuity is because when you factor out the denom. part of it is divided out and "removed". :D Does that help make better sense so far?

Answer 10

Ok yes it does!!

Answer 11

So can you help me with figuring out the rest of the prob?

Answer 12

Awesome. Now that you've simplified the question a bit, we have a new problem.. what can x= where it will again, be zero?

Answer 13

-3

Answer 14

so is -3 a non removable disconuntity?

Answer 15

and that is non-removable because we can't factor or anything like that anymore.

Answer 16

Correctamundo!

Answer 17

:D ok!

Answer 18

is that all I have to do then for this prob?

Answer 19

I believe so, it's just asking where it's discontinuous.

Answer 20

ok! what about the x values where f is not continuous

Answer 21

or do I already have that?

Answer 22

That is just what we found :D

Answer 23

ok thanks so much

Answer 24

It was basically asking you to find removable and non-removable ones.

Answer 25

aka, all kinds. :D

Answer 26

ok cool

Answer 27

be sure to keep this in mind when integrating! you'll end up having to take limits at those points eventually.

Answer 28

OK!