Math's formulas, graphs and tables

MATHEMATICS Formulas, Graphs, Tables, . . . < High School to University Level >

CONTENTS K

101 Use of differential to approximate the value of a function

Use of differential to approximate the value of a function examples

Rules for differentials

Differentials of some basic functions

Differentials of some basic functions examples

102 Higher order derivatives and higher order differentials

Higher order derivatives

Higher order derivatives examples

103 Higher derivative formula for the product - Leibniz formula

Higher derivatives of composite functions

Higher derivatives of composite functions examples

Higher derivatives of implicit functions

Higher derivatives of implicit function example

104 Higher derivatives of parametric functions

Higher derivatives of parametric functions

Higher derivatives of parametric functions examples

Higher order differentials

Higher order differentials examples

105 Applications of differentiation - the graph of a function and its derivative

Definition of increasing and decreasing of a function

Increasing/decreasing test

Rolle's theorem

The mean value theorem

Generalization of the mean value theorem

Cauchy's mean value theorem or generalized mean value theorem

106 L'Hospital's rule - limits of indeterminate forms

Applications of L'Hospital's rule - evaluation of limits of indeterminate forms examples

107 Generalization of the mean value theorem, concavity of the graph of a curve

Concavity of the graph of a function

Concave up and concave down definition

108 Points of inflection of a function

Points of inflection and concavity of the sine function example

Point of inflection and concavity of the cubic polynomial example

109 Approximate solution to an equation, Newton's method (or the Newton-Raphson method)

Use of Newton's method, example

110 Taylor's theorem (Taylor's formula) - The extended mean value theorem

Maclaurin's formula or Maclaurin's theorem