# Thread: Limits that exist and dont

1. ## Limits that exist and dont

Why can a limit be 0/0 and still exist. I know that you can simplify it, but what is the reason it exists?

2. Originally Posted by Newskin01
Why can a limit be 0/0 and still exist. I know that you can simplify it, but what is the reason it exists?
A limit doesn't have to be continuous at a point to exist. The LHS and RHS limits need to be equal for the limit to exist.

3. Originally Posted by Newskin01
Why can a limit be 0/0 and still exist, but what is the reason it exists?
Because, limits are about what happens to a function near a point.
We never consider the value at the point.

4. Originally Posted by Newskin01
Why can a limit be 0/0 and still exist. I know that you can simplify it, but what is the reason it exists?
an existent limit that yields the indeterminate form 0/0 upon direct substitution has a "hole" (a point discontinuity) at the limit value.

however, not all limits with the 0/0 indeterminate form exist ...

$\displaystyle \lim_{x \to 0} \frac{|x|}{x}$

5. Originally Posted by Newskin01
Why can a limit be 0/0 and still exist. I know that you can simplify it, but what is the reason it exists?
Remember that 0/0 can mean any number (0x = 0) or no number. The type of equation will put an implicit constraint specifying the number if the limit exists (e.g. the limit as x approaches 0 for sinx/x)