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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/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_Variables/1.03%3A_Partial_Derivatives/1.3E%3A_Exercises_for_Section_1.3This page discusses exercises on calculating partial and higher-order derivatives of functions, including limit definitions, surface plot analysis, and practical applications like volume and area. It ...This page discusses exercises on calculating partial and higher-order derivatives of functions, including limit definitions, surface plot analysis, and practical applications like volume and area. It also covers problems in differential calculus, such as finding points where partial derivatives equal zero, verifying Laplace's and heat equations, and analyzing rates of change in contexts like dimensions and productivity functions. Answers to the various exercises are provided throughout.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.07%3A_LHopitals_Rule/4.7E%3A_Exercises_for_Section_4.7This page discusses various limit evaluations in calculus, focusing on different forms and techniques including L'Hôpital's Rule. It highlights key results, such as limits of exponential and logarithm...This page discusses various limit evaluations in calculus, focusing on different forms and techniques including L'Hôpital's Rule. It highlights key results, such as limits of exponential and logarithmic functions, along with polynomial expressions. Specific limits are solved, for example, limits approaching 1, 0, and infinity. The text also addresses scenarios where L'Hôpital's Rule is not directly applicable but suggests reformulations.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/01%3A_Functions_and_Graphs/1.02%3A_Basic_Classes_of_Functions/1.2E%3A_Exercises_for_Section_1.2This page presents exercises on mathematical concepts including slopes, equations in slope-intercept form, and polynomial analysis. It discusses functions, intercepts, and their real-world application...This page presents exercises on mathematical concepts including slopes, equations in slope-intercept form, and polynomial analysis. It discusses functions, intercepts, and their real-world applications such as depreciation and sales predictions. The content features calculations for piecewise and linear functions, evaluations of mathematical statements, and interpretations of values in practical contexts.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.08%3A_Exponential_Growth_and_DecayOne of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and con...One of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.03%3A_The_Method_of_Undetermined_Coefficients_II/3.3E%3A_Exercises_for_Section_3.3This page discusses exercises for finding particular solutions to second-order linear differential equations with variable coefficients, including forms involving trigonometric and exponential functio...This page discusses exercises for finding particular solutions to second-order linear differential equations with variable coefficients, including forms involving trigonometric and exponential functions. It covers the derivation and verification of key formulas, establishing conditions for polynomial functions as solutions, and validates theorems connecting polynomial equations to solutions.
