0
$\begingroup$

I got this question as an exercise by my teacher (I think it can't be solved).

I know that the function $f(x)=e^{x\sqrt{2x-1}}$ doesn't have roots. How can you approximate a root that doesn't exist?

How can I show that the root can't be approximated by this method (or any other for that matter)?

$\endgroup$
4
  • 1
    $\begingroup$ It’s enough to show that $f(1/2)=1$ and that $f$ is increasing in the domain. $\endgroup$
    – Paul
    Apr 24, 2020 at 19:41
  • $\begingroup$ @Paul I see, that means it has no roots. So the conclusion would be: we can't use the method because the function has no roots. Right? $\endgroup$
    – mathman
    Apr 24, 2020 at 19:45
  • 1
    $\begingroup$ Not just no roots, but does not have 0 as a limit either. You need to approach the value for fixed point iteration to work. $\endgroup$
    – Paul
    Apr 24, 2020 at 19:47
  • $\begingroup$ Understood, thank you. $\endgroup$
    – mathman
    Apr 24, 2020 at 21:06

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .