Calculus Option Question

[maroctam]

Hello can someone who has done / is doing the calculus (previously called series and differential equations) option please help me with this question:

Here's my opinion: there is no limit. I think this is the case because I cannot simplify the original expression and I assume that for all values of B (within its domain) this function would be periodic and hence has no limit. I've graphed this for different values of B and my initial thoughts seem to be correct. However I have no idea how to prove this, and l'Hôpital's rule isn't helping...

All help is appreciated, thank you!!

(I would have asked this on the math question thread, but people don't seem to be very active there... I asked a question there a month or so ago and never got an answer, so I deleted it.)

[Rigel]

This does seem like a really weird limit. I can't find any of the indeterminate forms which call for L'Hopital's rule (as the function is periodic). Have you tried changing the tangent into terms of cosine and sine and separating the limit? (that is making lim x-> 00 a - lim x-> 00 b where a - b is your original function).

[maroctam]

This does seem like a really weird limit. I can't find any of the indeterminate forms which call for L'Hopital's rule (as the function is periodic). Have you tried changing the tangent into terms of cosine and sine and separating the limit? (that is making lim x-> 00 a - lim x-> 00 b where a - b is your original function).

Thanks for your reply, but I tried and it still doesn't lead anywhere....

[flinquinnster]

I agree that the question you posted does look distinctly weird - and I too don't think separating it will lead to anything productive. I'm wondering if you might have gotten a typo in this question - there was an identical question to this one in the November 2006 paper 3 - everything identical BUT it was asking for the limit as x approaches 0, which makes far more sense for a periodic trig function than for x approaches infinity. Although you do have to do L'Hopital's 3 times to get to a limit, you will eventually get there if you want to find x approaches 0. But for x approaches infinity, I can't see anything coming out of it.