• Support PF! Buy your school textbooks, materials and every day products Here!

Finding the nontrivial zeros of Tan x = x

  • Thread starter Firepanda
  • Start date
  • #1
430
0
2dj9zxz.png


I can do the first part no problem.

I then drew the graph, am I right in saying there is an infinite sequence because the lines intersect an infinite amount of times, because tan is periodic and has vertical asymptotes?

I have no idea about showing why the first non rivial zero is bounded like that. I would have thought the trivial zero was at the origin, and the first non trivial was in the range of 0<lambda<pi/2.

What am I not understanding here?

Thanks

edit:

oh I think I'm suppose to be looking for solutions in the range of pi and 3pi/2?
 

Answers and Replies

  • #2
dynamicsolo
Homework Helper
1,648
4
oh I think I'm suppose to be looking for solutions in the range of pi and 3pi/2?
...because [itex]\lambda[/itex] is a positive number, so the first non-trivial zero of the equation will be in the next quadrant where [itex]\tan \lambda[/itex] is positive, and you're after [itex]\lambda^{2}[/itex].

[EDIT: On thinking about this a little more, we could also go in the negative direction, since [itex]\tan \lambda [/itex] and [itex] \lambda [/itex] both have odd symmetry and we're looking for solutions for [itex]\lambda^{2}[/itex]... But it is easier to think about going in the positive direction.]

BTW, I think the problem-poser means the first non-trivial zero of the function [itex](\tan \lambda ) - \lambda [/itex] ; that last statement reads a little strangely...
 
Last edited:

Related Threads on Finding the nontrivial zeros of Tan x = x

Replies
1
Views
873
  • Last Post
Replies
18
Views
29K
Replies
5
Views
2K
Replies
1
Views
4K
  • Last Post
Replies
5
Views
5K
  • Last Post
Replies
14
Views
13K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
13
Views
1K
Replies
2
Views
1K
Top