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I've made it to the the final part of this question and got the expression with arctan in it:

However, I'm not sure what the final part is asking me to do. I know I've got to plug the new values into the right places, but I'm not sure what the end goal is. After putting in all the values $t_{\text{max}}$ and $U$ are both left and I don't know what to do, due to me not being able to do $\arctan(t)$ or $\tan(u)$ or anything. Anyway, any help would be appreciated.

HDE 226868
  • 2,354
Trev
  • 1
  • I think the question is asking you what the limit of this expression is as $u$ goes to infinity. – Joel Cohen Nov 16 '15 at 22:31
  • Hi, thanks for the input. I've seen that as u tends to infinity arctan tends to pi/2. I don't know how to formally show this though, because i just put increasingly large numbers into my calculator to i stayed at that figure. Substituting pi/2 for arctan(root((k/g)u)), I ended up with t is equal to or less than pi/(2root(gk))=0.7096 to 4 dp. Does that make sense at all? – Trev Nov 16 '15 at 23:16

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