I have this plot of $f(x)=\ln x$ and the tangent line at $x=e$, and I'd like to specify the
PlotRange so that it's the rectangle with its centroid at $(e,1)$, kind of like how
ViewCenter is used for 3D graphics. Supposing I'm plotting over $[0,2e]$, is there a good way to do this without manually determining the vertices of such a rectangle?
I'm trying to make this visual demonstration of linear approximations showing that, as you zoom in on the plot, the distance between the tangent and the curve gets smaller and smaller to the point of making it hard to distinguish between the two. So, on top of centering the plot, I'd like to use
Manipulate give the option of adjusting this zooming window, but I'm not sure how to set up the
PlotRange to begin with.