- #1
Demon117
- 165
- 1
I wanted to see what kind of responses I would get regarding this problem:
Let f : [tex]\Re[/tex][tex]\rightarrow[/tex][tex]\Re[/tex] be a continuous function that is differentiable for all nonzero x such that f '(x) exists. If f'(x) [tex]\rightarrow[/tex] L as x[tex]\rightarrow[/tex]0 exists, prove that f '(0) exists.
Let f : [tex]\Re[/tex][tex]\rightarrow[/tex][tex]\Re[/tex] be a continuous function that is differentiable for all nonzero x such that f '(x) exists. If f'(x) [tex]\rightarrow[/tex] L as x[tex]\rightarrow[/tex]0 exists, prove that f '(0) exists.