(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For all real numbers, f is a function satisfying |f(x)|<=|x|. Show that f is continuous at 0

2. Relevant equations

3. The attempt at a solution

Really stuck on this cause I'm confused with the absolute values on this function.

I *think* to show this you have to see if lim x>0+f(x) = lim x>0-f(x) = f(0) ?

And I tried doing this:

-|x|<=f(x)<=|x|

lim x>0+|x|=0

lim x>0- -|x|=0

f(0)=|0|=0

So they're all equal to 0.

I don't know if this is right though...help?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: How to show that this function is continuous at 0?

**Physics Forums | Science Articles, Homework Help, Discussion**