Question

How do I check something is analytic.
C-R is necessary but not sufficient. i was told that I must also check if the partial derivatives are continuous. How would I do that?

Answer 1

This is the defination for continuity.Ofcourse this is true CR work only after all four function are continuous.Now for continuous always remember that polynomial functions are continuous ,trigonometric function are continuous so for give function we need to notice only those points for which given function is not continuous.For ecample For a Rational function given function fail to be continuous when denominator is equal to zero.So we need to remember such type of points not the whole continuous concept.It occur 1-2 % when our function fail to be continuous else we have always continuous functions.