f(x)= ln x/(x-1), if 0<x not =1
c , if x=1
and what kind of discontinuity is present if c does not have this value?
can someone help me with this problem?
It is done by \neq
[LaTeX ERROR: Convert failed]
For the question at hand, you need to determine a value c such that the function is continuous. One way could be to just plug in 1 in the above definition with the natural log, but you cannot do that since you'd get something of the form 0/0. Hence you need to find the limit of [LaTeX ERROR: Convert failed] as x approaches 1. Or more succinctly, find
[LaTeX ERROR: Convert failed]
Once you find that, you can just set c equal to it. From the definitions of continuous functions, f(x) is continuous at point a if
[LaTeX ERROR: Convert failed]