Thread: Find Discontinuity And Classifying Them

The problem I am looking at is

I found that f was not defined at

I have -3 as a non-removable discontinuity, and 3 as a removable discontinuity, approaching positive infinity from either side. Yet, when I graph the function, it is unequivocally approaching a finite value. Why did limiting process give me positive infinity?

Originally Posted by Bashyboy

The problem I am looking at is

I found that f was not defined at

I have -3 as a non-removable discontinuity, and 3 as a removable discontinuity, approaching positive infinity from either side. Yet, when I graph the function, it is unequivocally approaching a finite value. Why did limiting process give me positive infinity?

Notice that if , we have



The left hand limit as is while the right hand limit as is . Since the left and right hand limits are not equal, this is a jump discontinuity.

Oh, so you can cancel out factors; I thought I remembered my teacher saying we couldn't, or maybe that was just in the original function.

Originally Posted by Bashyboy

Oh, so you can cancel out factors; I thought I remembered my teacher saying we couldn't, or maybe that was just in the original function.

You can cancel out factors as long as you realise that there is an extra discontinuity in your original function.