Question

Proof Assistance please!!

Answer 1

\(Suppose~that~f:[a,b] \rightarrow \Re ~is ~differentiable~and~c ~\epsilon ~[a,b].\)\(~~Then ~show~that~there~exists~a~sequence~{x_n},~x_n \not=c,\)\(~such~that~f'(c)=lim_{{n \rightarrow \infty}}f'(x_n).\)

Answer 2

@Hero , @nincompoop any ideas?

Answer 3

text not appearing???

Answer 4

We cant view the complete question. Please post again.

Answer 5

ok \[Suppose~that~f:[a,b] \rightarrow \Re ~is ~differentiable~and~c ~\epsilon ~[a,b].~~Then ~show~that~there~exists~a~sequence~{x_n},~x_n \not =c,~such~that~f'(c)=lim{n}{\inf}f'(x_n).\] Did that work?

Answer 6

No it did not. Its visible only up "then show that there...."

Answer 7

ok what can you see up to on the first post?

Answer 8

"....Then show that" can you start from here

Answer 9

\[Then ~show~that~there~exists~a~sequence~{x_n},~x_n \not =c,~such~that~f'(c)=lim_{n\rightarrow \infty}f'(x_n).\]

Answer 10

\[f'(c)=lim_{n \rightarrow \infty}f'(x_n).\]

Answer 11

I think I need to use the Mean Value Theorem?

Answer 12

I would define an Xn = c/(1 + 1/n) then lim Xn = c and lim f'(Xn) = F'(c) but the mean value theorem may be a more rigorous idea

Answer 13

ok thank you, I appreciate the input