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  • TitlePage
    https://math.libretexts.org/Workbench/Calculus_II%3A_Integral_Calculus/00%3A_Front_Matter/01%3A_TitlePage
    Calculus II: Integral Calculus ( CC BY-SA; Via Wikimedia)
  • 3.10: Chapter 3 Review Exercises
    https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.10%3A_Chapter_3_Review_Exercises
    This 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.
  • 4.1: Related Rates
    https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.01%3A_Related_Rates
    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 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.
  • 1: Functions and Graphs
    https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/01%3A_Functions_and_Graphs
    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 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.
  • 4.3: Chapter 4 Review Exercises
    https://math.libretexts.org/Workbench/Calculus_II%3A_Integral_Calculus/04%3A_Parametric_Equations/4.03%3A_Chapter_4_Review_Exercises
    The arc length of the spiral given by r=θ2 for 0≤θ≤3π is 94π3 units. Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve...The arc length of the spiral given by r=θ2 for 0≤θ≤3π is 94π3 units. Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve. x=1+t,y=t2−1,−1≤t≤1 x=et,y=1−e3t,0≤t≤1 Find the equation of the tangent line to the given curve. Find dydx,dxdy, and d2xdy2 of y=(2+e−t),x=1−sint Find the arc length of the curve over the given interval.
  • 3: Derivatives
    https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives
    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, 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.
  • Math 3A: Calculus 1 (Sklar)
    https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_1_(Sklar)
    This is the first part of the three-semester calculus sequence. Topics include functions, limits, continuity, differentiation and integration, and applications for polynomial and transcendental functi...This is the first part of the three-semester calculus sequence. Topics include functions, limits, continuity, differentiation and integration, and applications for polynomial and transcendental functions.
  • Math 3AC: Analytic Geometry and Calculus I
    https://math.libretexts.org/Courses/Irvine_Valley_College/Math_3AC%3A_Analytic_Geometry_and_Calculus_I
    A new take on the classic mathematical approach of learning Precalculus and Calculus separately, this book merges the two topics together. Using calculus notation to inspire the precalculus examples h...A new take on the classic mathematical approach of learning Precalculus and Calculus separately, this book merges the two topics together. Using calculus notation to inspire the precalculus examples helps students of either a Precalculus or Calculus with support course.
  • 2.4E: Exercises for Section 2.4
    https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/02%3A_Limits/2.04%3A_Continuity/2.4E%3A_Exercises_for_Section_2.4
    This page focuses on exercises related to continuity and discontinuities in functions, emphasizing classifications like removable, jump, and infinite discontinuities. It discusses piecewise functions,...This page focuses on exercises related to continuity and discontinuities in functions, emphasizing classifications like removable, jump, and infinite discontinuities. It discusses piecewise functions, the Intermediate Value Theorem, and applies Coulomb’s law to analyze continuity in physical contexts. Specific functions such as F(d), f(θ)=sinθ, and g(x)=|x| are examined for continuity.
  • 4.7: L’Hôpital’s Rule
    https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.07%3A_LHopitals_Rule
    In this section, we examine a powerful tool for evaluating limits. This tool, known as L’Hôpital’s rule, uses derivatives to calculate limits. With this rule, we will be able to evaluate many limits w...In this section, we examine a powerful tool for evaluating limits. This tool, known as L’Hôpital’s rule, uses derivatives to calculate limits. With this rule, we will be able to evaluate many limits we have not yet been able to determine. Instead of relying on numerical evidence to conjecture that a limit exists, we will be able to show definitively that a limit exists and to determine its exact value.
  • 4.4: The Mean Value Theorem
    https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.04%3A_The_Mean_Value_Theorem
    The Mean Value Theorem is one of the most important theorems in calculus. We look at some of its implications at the end of this section. First, let’s start with a special case of the Mean Value Theor...The Mean Value Theorem is one of the most important theorems in calculus. We look at some of its implications at the end of this section. First, let’s start with a special case of the Mean Value Theorem, called Rolle’s theorem.

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