Question

Find discontinuities of this function...

Answer 1

\[y = \ln(\frac{ x^3 -x^2 }{ x-1 })\]

Answer 2

Calculus?

Answer 3

sure

Answer 4

Well you'll clearly have one at 0.

Answer 5

You COULD have one at 1, but if you do the limit, it converges to 1, which is okay. So it appears to only be discontinuous at x = 0.

Answer 6

what is your reasoning?

Answer 7

ln is undefined at 0. Try to make the numerator not 0. There will be a kink or crease there at x = 0.

Answer 8

at wouldn't it be undefined at 1 as well?

Answer 9

The only other value that could make that 0 is 1, but there you get ln(0/0), which is indeterminiate

Answer 10

So work the limit, you'll see it actually converges on 1.

Answer 11

k thanks.

Answer 12

Or ln(1) which is 0, but point being...it's defined.