Question

How can you tell the difference between an undefined limit and a limit that does not exist from simply an equation that does not provide a graph?

Answer 1

You should have a general understand of certain functions. It usually comes with time.
Certain functions like ln(x) don't exist when x less than or equal to 0. Functions like tan(x) only exist -pi/2 < x < pi/2 and is periodic. There are infinitely many different functions but most of them are similar. You'll deal with trig functions (cos(x), sin(x), tan(x) etc) transcendental functions (e^{x} ln(x) ) and polynomials (ax^n + bx^(n-1) +...+x + c)

Answer 2

alright thanx