# Continuous functions help

• Mar 3rd 2010, 05:41 AM
tottijohn
Continuous functions help
In the following question, k =0.5.

http://img19.imageshack.us/img19/3323/cma3q11.gif

I know how to prove the function but am unsure which part is the answer. Any help?

-1 ≤ sin(1/2x) ≤ 1, for any x ≠ 0

-xsqr ≤ xsqr sin(1/2x) ≤ xsqr, for any x ≠ 0

g(x)[= -xsqr] ≤ f(x) ≤ [xsqr =]h(x), for any x ∈ ℝ

As the functions satisfied all 3 conditions of the squeeze rule, f is continuous at 0.

p/s: Sorry, i can't seem to get the square symbol working properly.
• Mar 3rd 2010, 05:46 AM
Krizalid
the image is missing, you're gonna have to fix that.
• Mar 3rd 2010, 08:11 AM
tottijohn
Fixed. Can you see it now?
• Mar 3rd 2010, 10:16 AM
Krizalid
yes, it's right.
• Mar 4th 2010, 06:51 AM
tottijohn
Thanks.

Anyone can help me out with this?
• Mar 4th 2010, 07:34 AM
Krizalid
haha, when i said that, i tacitly told you it's correct.
• Mar 5th 2010, 09:06 PM
tottijohn
Quote:

Originally Posted by Krizalid
haha, when i said that, i tacitly told you it's correct.

Haha, thanks for clarifying.

The qn here is asking for the lim f(x) which i am not sure.
My lecturer said it is not 0.
• Mar 5th 2010, 09:40 PM
TheEmptySet
Quote:

Originally Posted by tottijohn
Haha, thanks for clarifying.

The qn here is asking for the lim f(x) which i am not sure.
My lecturer said it is not 0.