1. ## Continuity question

So, the question asks; If F(x) = x^2sin(π/x), prove that f(0) can be defined in such a way that f becomes continous at x = 0.

I know for continuity you need to prove that the limit F(x) exists. So I used the squeeze theroem and found that the limit as x approaches 0 is 0.

I am having trouble proving that f(0) is defined. I know this is probably a stupid question but I just hit a math road block.

-Sterwine

2. Originally Posted by Sterwine
So, the question asks; If F(x) = x^2sin(π/x), prove that f(0) can be defined in such a way that f becomes continous at x = 0.

I know for continuity you need to prove that the limit F(x) exists. So I used the squeeze theroem and found that the limit as x approaches 0 is 0.

I am having trouble proving that f(0) is defined. I know this is probably a stupid question but I just hit a math road block.

-Sterwine
$\displaystyle -x^2 \le x^2\sin\left(\frac{\pi}{x}\right) \le x^2$

$\displaystyle y = -x^2$ and $\displaystyle y = x^2$ both equal 0 at $\displaystyle x = 0$

the question is not asking you to prove if f(0) is defined at x = 0, it isn't ... yet.
the question is asking how you would define f(0) to make the function continuous.

why do you think they call it a "removable" discontinuity?

3. Ah, thats exactly what I got, I guess I was just confused and read the question wrong.

Thank you very much