Expert: Chen Min - 1/4/2011

Question
what is a discontinuity, and how do i approximate it to three decimal places? e.g. f(x)=(x+1)/(x^2+2x-5) and
f(x)= (x+3)/|2sinx-x|

Answer
I don't understand what you are asking...

Firstly, discontinuity means a sudden jump/drop in the value of the function as it progresses along the x axis. It's not a value in itself but a property of the function at that certain point. So I have no idea how to "approximate it". For details and classifications just go to wikipedia.

Secondly, the examples you gave do not involve discontinuity but SINGULARITY (also just wiki it) because they are both undefined at a certain point when denominators are zero (x^2+2x-5=0,etc) If you draw out the graphs you'll see the function gets to infinity at both sides of the singularity.

Hope you can clarify it, or glean as much from the above.