Data from an experiment may result in a graph indicating exponential growth. This implies the formula of this growth is \(y = k{x^n}\), where \(k\) and \(n\) are constants. Using logarithms, we can ...

In the Introduction to the Derivative video we introduce the notion of the derivative of a function and explain how the derivative captures the instantaneous rate of change of a function. In the ...

Concepts covered in this course include: standard functions and their graphs, limits, continuity, tangents, derivatives, the definite integral, and the fundamental theorem of calculus. Formulas for ...

In this article, we prove an inequality between the ratio of the extended logarithmic means and the ratio of the exponential means. The proof is based on an inequality between logarithmic mean and one ...

The skills tested on this examination are a small subset of the skills that you should have learned in Calculus I. Passing this test quickly is very important since if you do not pass this test ...

THE authors of this volume have taken for their aim the axiom that the best preparation for the calculus is a suitable course in co-ordinate geometry. The text is thus divided into two sections: the ...

The information and materials presented here are intended to provide a description of the course goals for current and prospective students as well as others who are interested in our courses. It is ...

\({\log _a}a = 1\) (since \({a^1} = a\)) so \({\log _7}7 = 1\) \({\log _a}1 = 0\) (since \({a^0} = 1\)) so \({\log _{20}}1 = 0\) \({\log _a}p + {\log _a}q = {\log _a ...