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- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/12%3A_Introduction_to_Calculus/12.05%3A_DerivativesChange divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we...Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/12%3A_Introduction_to_CalculusCalculus is the broad area of mathematics dealing with such topics as instantaneous rates of change, areas under curves, and sequences and series. Underlying all of these topics is the concept of a li...Calculus is the broad area of mathematics dealing with such topics as instantaneous rates of change, areas under curves, and sequences and series. Underlying all of these topics is the concept of a limit, which consists of analyzing the behavior of a function at points ever closer to a particular point, but without ever actually reaching that point. Calculus has two basic applications: differential calculus and integral calculus.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/01%3A_Functions/1.03%3A_Domain_and_RangeIn creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this se...In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section, we will investigate methods for determining the domain and range of functions.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/09%3A_Systems_of_Equations_and_Inequalities/9.05%3A_Partial_FractionsDecompose a ratio of polynomials by writing the partial fractions. Solve by clearing the fractions, expanding the right side, collecting like terms, and setting corresponding coefficients equal to eac...Decompose a ratio of polynomials by writing the partial fractions. Solve by clearing the fractions, expanding the right side, collecting like terms, and setting corresponding coefficients equal to each other, then setting up and solving a system of equations. The decomposition with repeated linear factors must account for the factors of the denominator in increasing powers. The decomposition with a nonrepeated irreducible quadratic factor needs a linear numerator over the quadratic factor.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/08%3A_Further_Applications_of_Trigonometry/8.E%3A_Further_Applications_of_Trigonometry_(Exercises)If the angle of elevation from the man to the balloon is 27∘, and the angle of elevation from the woman to the balloon is 41∘, find the altitude of the balloon to the nearest foo...If the angle of elevation from the man to the balloon is 27∘, and the angle of elevation from the woman to the balloon is 41∘, find the altitude of the balloon to the nearest foot. For polar coordinates, the point in the plane depends on the angle from the positive x-axis and distance from the origin, while in Cartesian coordinates, the point represents the horizontal and vertical distances from the origin.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_223_Calculus_3/01%3A_Vectors_in_SpaceA quantity that has magnitude and direction is called a vector. Vectors have many real-life applications, including situations involving force or velocity. For example, consider the forces acting on a...A quantity that has magnitude and direction is called a vector. Vectors have many real-life applications, including situations involving force or velocity. For example, consider the forces acting on a boat crossing a river. The boat’s motor generates a force in one direction, and the current of the river generates a force in another direction. Both forces are vectors. We must take both the magnitude and direction of each force into account if we want to know where the boat will go.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/09%3A_Systems_of_Equations_and_Inequalities/9.01%3A_Prelude_to_Systems_of_Equations_and_InequalitiesIn this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. First, however, we will study systems of equations on their own: linea...In this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. First, however, we will study systems of equations on their own: linear and nonlinear, and then partial fractions. We will not be breaking any secret codes here, but we will lay the foundation for future courses.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/08%3A_Further_Applications_of_Trigonometry/8.07%3A_Parametric_EquationsWe begin this section with a look at the basic components of parametric equations and what it means to parameterize a curve. Then we will learn how to eliminate the parameter, translate the equations ...We begin this section with a look at the basic components of parametric equations and what it means to parameterize a curve. Then we will learn how to eliminate the parameter, translate the equations of a curve defined parametrically into rectangular equations, and find the parametric equations for curves defined by rectangular equations.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/02%3A_Limits/2.05%3A_Continuity/2.5E%3A_Exercises_for_Section_2.5It is given by the equation F(r)=ke|q1q2|r2, where ke is Coulomb’s constant, qi are the magnitudes of the charges of the two particles, and r is the distance between th...It is given by the equation F(r)=ke|q1q2|r2, where ke is Coulomb’s constant, qi are the magnitudes of the charges of the two particles, and r is the distance between the two particles. The force of gravity on the rocket is given by F(d)=−mk/d2, where m is the mass of the rocket, d is the distance of the rocket from the center of Earth, and k is a constant.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/02%3A_Limits/2.01%3A_Prelude_to_LimitsWe begin this chapter by examining why limits are so important. Then, we go on to describe how to find the limit of a function at a given point. Not all functions have limits at all points, and we dis...We begin this chapter by examining why limits are so important. Then, we go on to describe how to find the limit of a function at a given point. Not all functions have limits at all points, and we discuss what this means and how we can tell if a function does or does not have a limit at a particular value. The last section of this chapter presents the more precise definition of a limit and shows how to prove whether a function has a limit.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/01%3A_Functions_and_Graphs/1.07%3A_Chapter_1_Review_ExercisesFor the following problems, determine the largest domain on which the function is one-to-one and find the inverse on that domain. Find the equation C=f(x) that describes the total cost as a functi...For the following problems, determine the largest domain on which the function is one-to-one and find the inverse on that domain. Find the equation C=f(x) that describes the total cost as a function of number of shirts and Carbon dating is implemented to determine how old the skeleton is by using the equation y=ert, where y is the percentage of radiocarbon still present in the material, t is the number of years passed, and r=−0.0001210 is the decay rate of radiocarbon.
