A while back I ran into a problem in which I had to analyze the graph of $f(x) = ( \arctan x )^2$.
I was fine until I had to evaluate the limit of the function as is approaches infinity to determine if there were asymptotes. I did not know how to solve this algebraically or analytically so I proceeded to try graphically. Still, I was having trouble so I decided to ask a Calculus teacher at my school, but even then the teacher proceded to tell me that "you don't need to do that" and "this is past what we are doing in class" Obviously I am not just going to stop self studying math, I have been doing it for about 2 months now and I am not planning on stopping just because I am struggling with one concept so far. So after a while of trying to find a way to solve this I decided to move on. To my amusement one of these problem appeared again and now I need to understand this if I am ever going to proceed with my studies. The problem is an example from my textbook. The question says "Apply the Integral Test to the series $1/(n^2+1)$. I integrate and get the limit as b approaches infinity of [arctanb-arctan1]. At that point I am stuck.... The answer is given to be $\pi/2-\pi/4$ which is equal $\pi/4$. Please if anyone can shed some light on how to come about these answers.