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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/01%3A_Functions_and_GraphsIn this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, trigonometric, exponential, and logarithmic functions. We review how to evaluate these functio...In this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, trigonometric, exponential, and logarithmic functions. We review how to evaluate these functions, and we show the properties of their graphs. We provide examples of equations with terms involving these functions and illustrate the algebraic techniques necessary to solve them. In short, this chapter provides the foundation for the material to come.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/05%3A_Graph_Theory
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_VariablesWhen dealing with a function of more than one independent variable, several questions naturally arise. For example, how do we calculate limits of functions of more than one variable? The definition of...When dealing with a function of more than one independent variable, several questions naturally arise. For example, how do we calculate limits of functions of more than one variable? The definition of derivative we used before involved a limit. Does the new definition of derivative involve limits as well? Do the rules of differentiation apply in this context? Can we find relative extrema of functions using derivatives? All these questions are answered in this chapter.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_Through_Guided_Discovery_(Bogart)/02%3A__Induction_and_Recursion/2.03%3A_Graph_and_TreesIn Section 1.3.4 we introduced the idea of a directed graph. Graphs consist of vertices and edges. We describe vertices and edges in much the same way as we describe points and lines in geometry: we d...In Section 1.3.4 we introduced the idea of a directed graph. Graphs consist of vertices and edges. We describe vertices and edges in much the same way as we describe points and lines in geometry: we don’t really say what vertices and edges are, but we say what they do. We just don’t have a complicated axiom system the way we do in geometry. A graph consists of a set V called a vertex set and a set E called an edge set. Each member of V is called a vertex and each member of E is called an edge.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.06%3A_Limits_at_Infinity_and_Asymptotes/4.6E%3A_Exercises_for_Section_4.6This page offers exercises on identifying and evaluating vertical and horizontal asymptotes in mathematical functions and limits. It provides graphs showcasing asymptotic behavior, calculations for de...This page offers exercises on identifying and evaluating vertical and horizontal asymptotes in mathematical functions and limits. It provides graphs showcasing asymptotic behavior, calculations for determining the presence of asymptotes, and evaluations of limits as \(x\) approaches extreme values. The text discusses properties of various functions, including local maxima, minima, and inflection points, while outlining conditions for asymptote definitions.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.01%3A_Areas_between_Curves/2.1E%3A_Exercises_for_Section_2.1This page provides exercises on determining areas between curves through integration, covering various function types and methods. It includes analyses of different pairs of curves, calculations of ar...This page provides exercises on determining areas between curves through integration, covering various function types and methods. It includes analyses of different pairs of curves, calculations of area, and practical applications like marginal costs and revenues. The text features geometric representations and specific examples, including a business scenario related to profits and a comparison of speed functions in a race.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/05%3A_Graph_Theory/5.01%3A_Discovering_GraphsThis page explains how to define graphs through various properties, using examples and checkpoints to distinguish valid graph formations from invalid ones. It employs set notation and prompts readers ...This page explains how to define graphs through various properties, using examples and checkpoints to distinguish valid graph formations from invalid ones. It employs set notation and prompts readers to analyze necessary and forbidden properties of graphs, facilitating a translation between set forms and diagrams.
