# Finding limit of discontinous function (graph)

• Mar 30th 2010, 07:13 PM
tottijohn
Finding limit of discontinous function (graph)
Hi, i have this question which i am unsure whether the answer is 0 or 2.

If x tend to 2-, I know the limit is 2.

http://img232.imageshack.us/img232/2...0cma120q10.gif
• Mar 30th 2010, 08:02 PM
Prove It
Quote:

Originally Posted by tottijohn
Hi, i have this question which i am unsure whether the answer is 0 or 2.

If x tend to 2-, I know the limit is 2.

http://img232.imageshack.us/img232/2...0cma120q10.gif

What value does the function tend to if you make $\displaystyle x$ approach $\displaystyle 2$ from the right?
• Mar 30th 2010, 08:20 PM
tottijohn
0? But since 0 does not exist, is it 2?
• Mar 30th 2010, 09:38 PM
Prove It
You are finding out what $\displaystyle f(x)$ APPROACHES as you are making $\displaystyle x$ approach a value. That value of $\displaystyle f(x)$ need not be defined.
If you look carefully at the definition of limit you will see that we require $\displaystyle |f(x)- L|< \epsilon$ only if $\displaystyle 0< |x- a|< \delta$. That "0< |x- a|" means that what happens at x= a is irrelevant. It is only what happens near the point (and, here, larger) that is important.
For example, f(x)= $\displaystyle x^2- 1$ has limit 3 as x goes to 2. Now define g(x) to be $\displaystyle x^2- 1$ as long as x is NOT equal to 2 and any value you want for x= 2. No matter what value you assign at x= 2, $\displaystyle \lim_{x\to 2} g(x)= 3$.