For the function , show that exists. What is the value?

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- August 8th 2010, 08:50 PMilovemymathDerivative
For the function , show that exists. What is the value?

- August 8th 2010, 09:12 PMGeneral
Do you know the limit definition of the derivative of the function at point ?

- August 8th 2010, 09:18 PMilovemymath
nop

- August 8th 2010, 09:42 PMeumyang
Hmm... you should! The derivative of f at c is

.

The existence of this limit in this form requires that the one-sided limits

and exist and are equal. I think you will have to evaluate both one-sided limits and show that they are equal in order to prove that f'(0) exists in your case.