# Homework Help: Finding removable and jump discontinuities

1. Oct 15, 2009

### DanielJackins

1. The problem statement, all variables and given/known data

f(x) = -x + b, if x < 2
= 5, if x = 2
= -20/(x-b) + 1, if x > 2

For what value(s) of b does f have a removable discontinuity at 2?
For what value(s) of b does f have a (finite) jump discontinuity at 2? Write your answer in interval notation.

3. The attempt at a solution

I'm completely stumped on the removable discontinuity, because I thought you had to be able to cancel out the bottom?

And I'm not sure how to find a jump discontinuity.

2. Oct 15, 2009

### Dick

A removable discontinuity is a value of b where the limit as x->2 from below and the limit as x->2 from above are equal. Your first job is to find those two limits in terms of b. Then equate them. Can you do that?

3. Oct 15, 2009

### DanielJackins

Are the limits not -inf and inf?

4. Oct 15, 2009

### Dick

No. The limits as x->2! The limit from above is (x>2) is -20/(2-b)+1, isn't it? What's the limit from below?