how many times can we differentiate this splitted function on point x=0

??

{0,x=0}

i did one differentiation

what to do next??

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- February 5th 2009, 11:11 PMtransgalactichow many times can we differentiate this function??
how many times can we differentiate this splitted function on point x=0

??

{0,x=0}

i did one differentiation

what to do next??

- February 5th 2009, 11:52 PMAbu-Khalil
You asumme or was an error?

Anyway, knowing that, you may define the derivate function of as .

And now you have problems because doesn't converge. - February 7th 2009, 11:50 PMtransgalactic
what is the correct way of proving it??

- February 8th 2009, 08:02 AMHallsofIvy
Proving what? That does not exist? That should be obvious: cos(1/x) is always between -1 and 1 and the denominator goes to 0 so that term does not converge. 2 sin(1/x) is always between -2 and 2 so it cannot "offset" the fact that cos(1/x)/x diverges.

- February 8th 2009, 09:30 AMtransgalactic
i got a different result.

i assumed that in point x=0 the function turns to 0 too.

so in the plus side i will get 0

and on the minus side

but i cant keep doing this derivatives till i get two different limits

there must be an easier way

??