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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/05%3A_Differential_Calculus_with_Parametric_Curves/5.01%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.01%3A_Related_Rates/4.1E%3A_Exercises_for_Section_4.1This page contains exercises on related rates in calculus, focusing on finding time derivatives for varying scenarios such as motion and geometry. It includes problems about a ladder, moving airplanes...This page contains exercises on related rates in calculus, focusing on finding time derivatives for varying scenarios such as motion and geometry. It includes problems about a ladder, moving airplanes, and geometric shapes filled with water, addressing changes in volume, height, and angle. The text requires diagrams for clarity and concludes each problem with calculated answers, enhancing understanding of rates of change in real-life situations.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/01%3A_Functions_and_Graphs/1.01%3A_Review_of_Functions/1.1E%3A_Exercises_for_Section_1.1This page contains exercises on analyzing relations and functions, focusing on determining domains and ranges, identifying functions through input-output tables, and sketching graphs. It discusses var...This page contains exercises on analyzing relations and functions, focusing on determining domains and ranges, identifying functions through input-output tables, and sketching graphs. It discusses various mathematical functions, particularly piecewise and polynomial graphs, employing the vertical line test and analyzing characteristics like symmetry and intercepts.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.10%3A_Chapter_3_Review_ExercisesThis page contains exercises on calculus derivatives, including evaluating derivatives, proving statements, and deriving tangent line equations. It emphasizes the interpretation of derivatives in prac...This page contains exercises on calculus derivatives, including evaluating derivatives, proving statements, and deriving tangent line equations. It emphasizes the interpretation of derivatives in practical contexts like water levels and wind speeds. The answer sections illustrate the connection between mathematical calculations and real-world applications by providing derivative functions and their evaluations at specific points.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.01%3A_Related_RatesIf two related quantities are changing over time, the rates at which the quantities change are related. For example, if a balloon is being filled with air, both the radius of the balloon and the volum...If two related quantities are changing over time, the rates at which the quantities change are related. For example, if a balloon is being filled with air, both the radius of the balloon and the volume of the balloon are increasing. In this section, we consider several problems in which two or more related quantities are changing and we study how to determine the relationship between the rates of change of these quantities.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/00%3A_Front_Matter/03%3A_Table_of_Contents
- 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/Calculus_I%3A_Differential_Calculus/zz%3A_Back_Matter/22%3A_Detailed_Licensing
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/zz%3A_Back_Matter/10%3A_Index
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_DerivativesCalculating velocity and changes in velocity are important uses of calculus, but it is far more widespread than that. Calculus is important in all branches of mathematics, science, and engineering, an...Calculating velocity and changes in velocity are important uses of calculus, but it is far more widespread than that. Calculus is important in all branches of mathematics, science, and engineering, and it is critical to analysis in business and health as well. In this chapter, we explore one of the main tools of calculus, the derivative, and show convenient ways to calculate derivatives. We apply these rules to a variety of functions in this chapter.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.06%3A_The_Chain_Rule/3.6E%3A_Exercises_for_Section_3.6This page covers exercises on applying the chain rule for differentiating composite functions and finding derivatives using Leibniz's notation. It includes systematic methods for calculating \(\frac{d...This page covers exercises on applying the chain rule for differentiating composite functions and finding derivatives using Leibniz's notation. It includes systematic methods for calculating dydx and finding tangent and normal lines. Additionally, it addresses problems in physics and calculus, emphasizing rates of change in motion, with applications in velocity, acceleration, and geometric changes.
