Add to ORKGThe Intermediate Value Theorem (a continuous function on an interval assumes all values between any two of its values) is one of the big theorems of calculus. Yet the theorem is absent or briefly mentioned in most calculus textbooks. The theorem deserves better as we intend to show by listing ten picturesque consequences that we think could enliven any calculus course
CalculusIf the function f is continuous over the closed interval [a,b], then there is at least one m...
Abstract. In this paper, I will present some elementary definitions in Topol-ogy. In particular, I w...
Calculus and IntegralsThere is at least one point in the interval such that the area of the rectangl...
CalculusThe integral mean value theorem (a corollary of the intermediate value theorem) states that ...
Making the transition from calculus to advanced calculus/real analysis can be challenging for underg...
Let f be a real function defined on a bounded interval I: = [A,B]. The following well-known theorem ...
The solvability of nonlinear equations has awakened great interest among mathemati-cians for a numbe...
Any continuous function with values in a Hausdorff topological space has a closed graph and satisfie...
Abstract. The intermediate value theorem for a continuous real valued function is a kind of Bolzano&...
Abstract. A simple proof of a theorem unifying Bolzano's Theorem [8], the Intermediate Value Th...
summary:The aim of the paper is to present some mean value theorems obtained as consequences of the ...
This book includes over 500 most challenging exercises and problems in calculus. Topical problems an...
The Intermediate Value Theorem, Boundedness Theorem, Extreme Value Theorem, and Integrability Theore...
When you first took calculus, there were probably many things that you understood at a mostly intuit...
Abstract Stone Duality is a revolutionary paradigm for general topology that describes com-putable c...
CalculusIf the function f is continuous over the closed interval [a,b], then there is at least one m...
Abstract. In this paper, I will present some elementary definitions in Topol-ogy. In particular, I w...
Calculus and IntegralsThere is at least one point in the interval such that the area of the rectangl...
CalculusThe integral mean value theorem (a corollary of the intermediate value theorem) states that ...
Making the transition from calculus to advanced calculus/real analysis can be challenging for underg...
Let f be a real function defined on a bounded interval I: = [A,B]. The following well-known theorem ...
The solvability of nonlinear equations has awakened great interest among mathemati-cians for a numbe...
Any continuous function with values in a Hausdorff topological space has a closed graph and satisfie...
Abstract. The intermediate value theorem for a continuous real valued function is a kind of Bolzano&...
Abstract. A simple proof of a theorem unifying Bolzano's Theorem [8], the Intermediate Value Th...
summary:The aim of the paper is to present some mean value theorems obtained as consequences of the ...
This book includes over 500 most challenging exercises and problems in calculus. Topical problems an...
The Intermediate Value Theorem, Boundedness Theorem, Extreme Value Theorem, and Integrability Theore...
When you first took calculus, there were probably many things that you understood at a mostly intuit...
Abstract Stone Duality is a revolutionary paradigm for general topology that describes com-putable c...
CalculusIf the function f is continuous over the closed interval [a,b], then there is at least one m...
Abstract. In this paper, I will present some elementary definitions in Topol-ogy. In particular, I w...
Calculus and IntegralsThere is at least one point in the interval such that the area of the rectangl...