Question

A point at which a function ceases to be analytic is called a

Answer 1

A point at which a function ceases to be analytic is called a singular point.

A singular point on a graph of a function is a point where the curve of the function behaves in an extraordinary manner. A point on the curve is singular if the partial derivatives of the function are zero at that point.

An analytic function in mathematics can be defined as a function that is locally given by a convergent power series.

In the graph of a function when the function ceases to be analytic the graph changes and the point obtained is called a singular point.

Answer 2

A point at which a function ceases to be analytic is called a singular point.

• Explanation:
• The graph in which the curve of the function behaves in an extraordinary manner is known as a singular point.
• If the partial derivatives of the function are zero at any point The point on the curve is singular.
• Analytic at a point  is a function f is called z0 ∈ C if there exist r > 0 such that f is differentiable at every point z ∈ B(z0, r).
• If the function is analytic at each point U then a function is called analytic in an open set U ⊆ C.
• If the complex function is differentiable at every point It is said to be  analytic on a region.
• "Analytic function" are sometimes used interchangeably with  other terms holomorphic function, differentiable function, and complex differentiable function.

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