Question

determine if f has a removable discontinuity. show why.
1. f(x)=3x/abs(x) ... at x=0

Answer 1

Well certainly you can't have 0 on the bottom of the fraction, so we know that it is not continuous there. Also notice that you can cancel x on top and bottom. leaving you with f(x)=3. So it turns out that you have a HOLE at x=0. Everywhere else is going to be 3.

Answer 2

Oops i mean

Answer 3

After x>0, it's 3. But before x<0, it's -3.

Answer 4

And it's not a hole, it's a jump discontinuity, so there is no removable discontinuity

Answer 5

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