Hi,

I have a question:

I have the function :

f(x)=(X^(2n))*sin(1/x) when x is no 0, and f(x)=0 when x=0.

the question is how many times we can Derivative f(x) in x=0.

thanks to anyone that can help!

Printable View

- January 28th 2009, 08:54 AMomerbguDerivative
Hi,

I have a question:

I have the function :

f(x)=(X^(2n))*sin(1/x) when x is no 0, and f(x)=0 when x=0.

the question is how many times we can Derivative f(x) in x=0.

thanks to anyone that can help! - January 28th 2009, 09:22 AMcourteous
If both right and left limits (falling and rising to 0, respectively) of f(x) exist (and are same), then you can take derivative (you can differentiate) of f(x) at x=0, unlimited times.

- January 28th 2009, 10:54 AMomerbgu
hi,

how do you proof this??