- #1
Math Amateur
Gold Member
MHB
- 3,920
- 48
I need help with the proof of Apostol Theorem 5.2.
Theorem 5.2 and its proof read as follows:
https://www.physicsforums.com/attachments/3910
In the above proof, Apostol gives an expression or formula for $$f^*$$ and then states the following:
" ... ... Then $$f^*$$ is continuous at c ... ... "I need help with formulating a rigorous and formal demonstration that $$f^*$$ is continuous ...
Can someone please help?
Peter***EDIT***
Oh! Just had a thought regarding my question above ... ...
Presumably the demonstration I was looking for is simply the following ... ...$$ \lim_{x \to c} f^* (x) = \lim_{x \to c} \frac{f(x) - f(c)}{x-c} = f'(c) = f^*(c) $$
Can someone please confirm that this is correct?
Peter
Theorem 5.2 and its proof read as follows:
https://www.physicsforums.com/attachments/3910
In the above proof, Apostol gives an expression or formula for $$f^*$$ and then states the following:
" ... ... Then $$f^*$$ is continuous at c ... ... "I need help with formulating a rigorous and formal demonstration that $$f^*$$ is continuous ...
Can someone please help?
Peter***EDIT***
Oh! Just had a thought regarding my question above ... ...
Presumably the demonstration I was looking for is simply the following ... ...$$ \lim_{x \to c} f^* (x) = \lim_{x \to c} \frac{f(x) - f(c)}{x-c} = f'(c) = f^*(c) $$
Can someone please confirm that this is correct?
Peter
Last edited:
