# examples of the limit of f+g

• Mar 7th 2010, 08:07 PM
tn11631
examples of the limit of f+g
Does anyone know any examples that even though f and g fail to have limits at $\displaystyle x_0$, it is possible for f+g to have a limit at $\displaystyle x_0$, and examples for the same conditions but fg and f/g?
• Mar 7th 2010, 08:13 PM
Drexel28
Quote:

Originally Posted by tn11631
Does anyone know any examples that even though f and g fail to have limits at $\displaystyle x_0$, it is possible for f+g to have a limit at $\displaystyle x_0$, and examples for the same conditions but fg and f/g?

This is a common theme throughout intro. real analysis. You agree that there are functions $\displaystyle f$ which don't have limits, right? You agree that $\displaystyle \lim_{x\to x_0}0=0$ for any $\displaystyle x_0$, right? Combine the two.
• Mar 7th 2010, 08:15 PM
tn11631
Quote:

Originally Posted by Drexel28
This is a common theme throughout intro. real analysis. You agree that there are functions $\displaystyle f$ which don't have limits, right? You agree that $\displaystyle \lim_{x\to x_0}0=0$ for any $\displaystyle x_0$, right? Combine the two.

yea i think i figured out one example that works for all three. I tired to delete the thread right when i realized. Sorry!! but thank you.