# How to show a limit superimposed on a graph

GROUPS:
 Peter Brown 2 Votes I'd like to Plot the following graph with the Limit superimposed on it.  If I enter the following as freeform, then the suggestions back from Alpha include exactly the graph I'm looking for with a red circle showing the limit, but I can't figure out how to make Mathematica create the same chart.Plot[(x - 5)/(x^2 - 25), {x, -2.752, 12.752}]Limit[(x - 5)/(x^2 - 25), x -> 5]Any suggestions gratefully received.
5 years ago
4 Replies
 Arnoud Buzing 2 Votes First, set your xlim and ylim values:xlim = 5;ylim = Limit[(x - 5)/(x^2 - 25), x -> xlim];Then, use Epilog to draw a dot:Plot[(x - 5)/(x^2 - 25), {x, -2.752, 12.752}, Epilog -> {AbsolutePointSize[5], Red, Point[{xlim, ylim}]}]Or to draw a circle:Plot[(x - 5)/(x^2 - 25), {x, -2.752, 12.752}, Epilog -> {Red, Circle[{xlim, ylim}, Scaled[{.02/GoldenRatio, .02}]]}]Or something more fun:Plot[(x - 5)/(x^2 - 25), {x, -2.752, 12.752}, Epilog -> {Text[Style["\[FreakedSmiley]", 36], {xlim, ylim}]}]