# Math Help - Analysis

1. ## Analysis

I just could not figure out how to get epsilon at the end.

If f is continuous at a, and g is continuous at a, show that f+g is continuous at a.

2. Originally Posted by thahachaina
I just could not figure out how to get epsilon at the end.

If f is continuous at a, and g is continuous at a, show that f+g is continuous at a.
Hint: $|f(x)+g(x)-f(a)-g(a)| = |[f(x)-f(a)]+[g(x)-g(a)]| \leq |f(x)-f(a)|+|g(x)-g(a)|$

3. Thanks buddy. But thats what i did. and both the terms you get at the end is less than epsilon. So when u add up, you get 2 epsilon. Don't i need to get "epsilon" as opposed to "2epsilon". My prof is picky about that.

4. Originally Posted by thahachaina
Thanks buddy. But thats what i did. and both the terms you get at the end is less than epsilon. So when u add up, you get 2 epsilon. Don't i need to get "epsilon" as opposed to "2epsilon". My prof is picky about that.
Make both $|f(x)-f(a)|,|g(x)-g(a)|$ smaller than $\frac{\epsilon}{2}$.