hobz Posted July 7, 2010 Share Posted July 7, 2010 Suppose I have f(x)=e^x, how can it be proven that it is smooth? Link to comment Share on other sites More sharing options...
the tree Posted July 7, 2010 Share Posted July 7, 2010 A function is smooth if it has a derivative of all orders, so you simply have to find its derivatives for all orders. You should be able to prove that by induction. Link to comment Share on other sites More sharing options...
hobz Posted July 8, 2010 Author Share Posted July 8, 2010 I see! So the implicit requirement for a function to be smooth in order to be differentiable, can be used "in reverse" to find out if a function is smooth. This also implies that all smooth functions can be represented as a Taylor series? Link to comment Share on other sites More sharing options...
the tree Posted July 8, 2010 Share Posted July 8, 2010 Yes they can. Link to comment Share on other sites More sharing options...
hobz Posted July 9, 2010 Author Share Posted July 9, 2010 Thanks! Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now