Add to ORKGWe know that if a function is differentiable, then it is continuous. What, if anything, do we know about the continuity of that existing derivative? We shall examine elementary functions and an example of an existing derivative that is not continuous. Related facts, not usually a part of elementary calculus, will be discussed at an elementary level
A functional is a mapping from a set of functions to the set of real numbers. In this paper we estab...
It is shown conditions on derivatives can be expressed in a discrete manner without any requirements...
Green’s Theorem in multivariable calculus is usually stated with a hypothesis that the partial deriv...
We know that continuity is a necessary condition for the differentiability of a function. This may s...
AbstractUsing elementary ideas and techniques, we prove (Theorem 2) that for a nonconstant different...
The article provides a brief overview of the origin of the derivative, also discusses the issues tha...
AbstractThe derivative of a real, continuous function (and, in fact, of a more general one) can be d...
There are surprisingly many essentially different definitions of continuity even of a real function ...
Monotonicity of functions were of great interest of many mathematicians. Starting from the well know...
Definición y determinación de la continuidad de funciones.Definition and determination of continuous...
Continuity is relevant for the real numbers and functions, namely to understand singularities and ju...
We provide a simple example showing that the tangential derivative of a continuous function φ can va...
In the Diploma thesis we discuss the basic properties of functions of several variables. We focus on...
Contrary to intuition, functions exist that are continuous everywhere, but differentiable almost now...
Calculus and Analytic GeometryThis differentiation microscope lets you graphically explore if a func...
A functional is a mapping from a set of functions to the set of real numbers. In this paper we estab...
It is shown conditions on derivatives can be expressed in a discrete manner without any requirements...
Green’s Theorem in multivariable calculus is usually stated with a hypothesis that the partial deriv...
We know that continuity is a necessary condition for the differentiability of a function. This may s...
AbstractUsing elementary ideas and techniques, we prove (Theorem 2) that for a nonconstant different...
The article provides a brief overview of the origin of the derivative, also discusses the issues tha...
AbstractThe derivative of a real, continuous function (and, in fact, of a more general one) can be d...
There are surprisingly many essentially different definitions of continuity even of a real function ...
Monotonicity of functions were of great interest of many mathematicians. Starting from the well know...
Definición y determinación de la continuidad de funciones.Definition and determination of continuous...
Continuity is relevant for the real numbers and functions, namely to understand singularities and ju...
We provide a simple example showing that the tangential derivative of a continuous function φ can va...
In the Diploma thesis we discuss the basic properties of functions of several variables. We focus on...
Contrary to intuition, functions exist that are continuous everywhere, but differentiable almost now...
Calculus and Analytic GeometryThis differentiation microscope lets you graphically explore if a func...
A functional is a mapping from a set of functions to the set of real numbers. In this paper we estab...
It is shown conditions on derivatives can be expressed in a discrete manner without any requirements...
Green’s Theorem in multivariable calculus is usually stated with a hypothesis that the partial deriv...