Question

In problem set 1, question 1D-3c: Why does y=x^4/x^3 have a removable discontinuity at zero when y=x is continuous? Aren't they equivalent?

Answer 1

The domain is based on the original equation, and in this case in the denominator of your original equation you have x^3. If you substitute x=0 into the denominator you get zero. Anything over 0 is undefined.

The equation y=x is true when x !=(does not equal) 0

Answer 2

Understood, thanks