Thread: bounded function

Hello. I hope this is the right place to post this:

why is ⎮x⎮÷ (1+x^2)

bounded at 1/2 , meaning ≤ 1/2?

thanks a lot

notice that:



you can also easily find that the function has two symmetrical maxima points at 1 and -1

f(1) = f(-1) = 0.5 from the combination of these two facts we conclude that:

but then where is the 1/2 coming from?

Have you read my post carefully (f(1) = f(-1) = 0.5) ?

oh sorry. i did not see the second part when i posted it, it did not appear. it just appeared the part on the limit. i don't know how.

with the second part added is much better. now i got it
thanks!