# Thread: finding vertical asymptotes of a function

1. ## finding vertical asymptotes of a function

Would like to know where to start on this type of problem, since it's not a regular polynomial that i'm finding the asymptotes for. I'd like to know the process and any helpful tips for this kind of problem. I realize the solution is something along the lines of +-pi +-n(pi) (based on a similar example) but i'd appreciate a dumbed down explanation if possible.

problem (for simplicity i'll make x = theta):

Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary nonzero integer if necessary)

g(x) = (tan 4x)/(3x)

2. First find points where the function g(x) is not defined.

In this case they are x=0 and x=Pi/8 + k*(Pi/4)

Now find:

$\displaystyle \lim_{x \rightarrow 0} \frac{tan(4x)}{3x}$

and $\displaystyle \lim_{x \rightarrow \frac{\pi}{8}} \frac{tan(4x)}{3x}$

If the limit goes to infinity then there is vertical asymptote in the corresponding point.

Regards.

3. thanks, looks like the second one is approaching infinity. also wondering though how you find the candidate (other than zero), since i'm not sure how to find out when tan4x/3x = 0 in terms of unit circle. do i use sin/cos?

4. Yes, the second is approaching infinity so $\displaystyle x=Pi/8 + kPi/4$ will be all vertical asymptotes.

Tan(x) is not defined for Pi/2, therefore Tan(4x) will be not defined for Pi/8.

Regards.