Sketch the graph of y = x - arctanx, showing its asymptotes.
Now I got the correct shape of the graph, but my asymptotes were wrong.
I dont understand how you would get the asymptote of y = x + π/2 and y = x - π/2. Could someone please explain?
Sketch the graph of y = x - arctanx, showing its asymptotes.
Now I got the correct shape of the graph, but my asymptotes were wrong.
I dont understand how you would get the asymptote of y = x + π/2 and y = x - π/2. Could someone please explain?
Remember that tangent is not a one-to-one function (ie, it sends multiple points in its domain to the same point in its range). Thus, in order for arctangent to be a function, its range has to be restricted to $\displaystyle -\frac{\pi}{2} < x < \frac{\pi}{2} $, otherwise it would be multiply defined (without the restriction, where, for instance, would arctan(0) go?). So, to find the asymptotes, we need to find where the graph does not pass.
We know that $\displaystyle |arctan(x)| < \frac{\pi}{2} $, so where are those asymptotes?