Question

does the limit as x approaches 3 of |x-3|/x-3 exist? If so, can you show how you came to that conclusion.

Answer 1

no it doesn't

Answer 2

this is identically 1 if x > 3 and
-1 if x < 3.
limit from the left is -1, limit from the right is 1
and since those numbers are not the same, there is no limit at 3

Answer 3

thanks! i initially though that the limit didnt exist because i remember a previous example in class like this but i did not know how to prove it..thanks!

Answer 4

could you explain why it =1 if x>3 and why it is -1 if x<3 ?