Question 1082309
<pre>{{{matrix(2,1,lim,"x->5")}}}{{{(sqrt(x)-2)/(x-5)}}}

The limit does not exist because the denominator approaches 0
as x approaches 5, but the numerator approaches a finite number.

There is an asymptote on the graph of {{{"f(x)"}}}{{{""=""}}}{{{(sqrt(x)-2)/(x-5)}}} at 5, (the green dotted line).

{{{drawing(400,400,-2,8,-5,5,
green(line(5,4,5,5),line(5,2.5,5,3.5),line(5,1,5,2),line(5,.5,5,1.5),
line(5,-1,5,0),line(5,-2.5,5,-1.5),line(5,-4,5,-3),line(5,-5.5,5,-4.5)),

graph(400,400,-2,8,-5,5,(sqrt(x)-2)/(x-5)) )}}}

Edwin</pre>