Write all horizontal and vertical asymptotes for the function; list any removable discontinuities (holes). (If an answer does not exist, enter DNE.)
f(x)=tan^-1(x^2/(x+3))??

Question

Write all horizontal and vertical asymptotes for the function; list any removable discontinuities (holes). (If an answer does not exist, enter DNE.) 
f(x)=tan^-1(x^2/(x+3))??

jamesj · Answer

First of all, where is arctan defined and not defined?  I know the answer, I'm just trying to help by showing you steps, rather than blurting out the whole answer at once.

anonymous · Answer

hmm..well i figured it out except how to find discontinuities?

anonymous · Answer

ohh ok! but what about finding holes in it?

jamesj · Answer

Those are the 'holes'; those are the points of discontinuity in the function.

anonymous · Answer

hmmm...so what about the equation (x^2-3x)/(x^2-9)? im still a little confused :/

jamesj · Answer

Sorry, arctan, not tan. What is the domain of the function arctan? It's actually the entire real axis, from negative infinity to positive infinity. So the only 'hole' or point of discontinuity of this function is when x^2/(x+3) isn't defined. Namely, when x = -3. Now as x -> infinity, this term x^2/(x+3) -> infinity. And as x-> -infinity, x^2/(x+3) -> -infinity. Hence lim_{x->inf} f(x) = pi/2 and lim{x->-inf} f(x) = -pi/2. This will also help you: http://www.wolframalpha.com/input/?i=arctan%28x^2%2F%28x%2B3%29%29

anonymous · Answer

wait that last equation doesnt have tan or anything?