Cauchy-Riemann equations are satisfied for the function f(z) but f(z) is not analytic at origin

​‪@mathematicsbydr.sanjaysing1271‬ Lecture-7: Cauchy-Riemann equations are satisfied for the function f(z) but f(z) is not analytic at origin I Function f(z) is not analytic even though Cauchy- Riemann equations are satisfied at origin i.e.(0,0) Engineering Mathematics I Mathematics for Undergraduate and Post Graduate Students I IIT JAM I GATE I CSIR (NET) Your Queries: Partial Derivatives of u & v, where f(z)=u+iv Cauchy Riemann Equations at Origin i.e. (0,0) f(z) is not Differentiable at at Origin i.e. (0,0) Derivative of f(z) Does not Exist at Origin i.e. (0,0) How to Show f^'(0) Does Not Exist Cauchy Riemann Analytic Function Regular Function Holomorphic Function Cauchy Riemann Equations Cauchy Riemann Equations at origin i.e. (0,0) C-R Equations are satisfied but f(z) is not analytic at origin i.e. (0,0) Cauchy Riemann Equations are satisfied but f(z) is not analytic at z=0 f(z) is not analytic at origin i.e. (0,0) even though Cauchy Riemann equations are satisfied at origin i.e. (0,0) f(z) is not regular at origin i.e. (0,0) even though Cauchy Riemann equations are satisfied at origin i.e. (0,0) f(z) is not differentiable at origin i.e. (0,0) even though Cauchy Riemann equations are satisfied at origin i.e. (0,0) Necessary Condition for the Function to be Analytic Necessary Condition for Function f(z) Sufficient Condition for Function to be Analytic Sufficient Condition for Function f(z) How to Check Function f(z) is Analytic Method to Show f(z) is Analytic Analyticity of f(z) #Analytic Function #Regular Function #Holomorphic Function #Cauchy Riemann Equations #C-R Equations #Necessary Condition for the Function to be Analytic #Necessary Condition for Function f(z) #Sufficient Condition for Function to be Analytic #Sufficient Condition for Function f(z) #How to Check Function f(z) is Analytic #Method to Show f(z) is Analytic #Analyticity of f(z) Thanks for Watching and your Support Like, Share and Subscribe Dr. Sanjay Singh