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Differentiability... watch

1. f(x) = x^2 sin(1/x) for all x not equal to 0 and f(0)=0. Prove that f(x) is differentiable at x=0. ??!!!??

Thanks =]
2. |x^2 sin(1/x)| <= x^2
3. (Original post by DFranklin)
|x^2 sin(1/x)| <= x^2
I thought I had to use that the function is differentiable if
lim (h->0) [f(x+h) - f(x)]/h exists?
4. ooh do i use that equation and then the fact that |x^2 sin(1/x)| <= x^2 to evaluate the limit by squeeze theorem or something... would the limit be 0?
5. Yes, and yes.
6. (Original post by DFranklin)
Yes, and yes.
Awesome. Thank you
7. (Original post by DFranklin)
Yes, and yes.
=/ ah no, I'm actuall still stuck. I don't know how to put an inequality on the limit because it's one thing minus another..

wouldn't the smallest it can be, be the limit of - x^2 over h?
8. You're testing for differentiability at 0, so x = 0. You end up with |h^2 / h|.

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