- #1
nerdz4lyfe
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Homework Statement
For all real numbers, f is a function satisfying |f(x)|<=|x|. Show that f is continuous at 0
Homework Equations
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?