How is the ball moving? Questions like this one are central to our study of differential calculus. We begin with a simple problem: a ball is tossed straight up in the air. A natural and important question to ask about any changing quantity is “how fast is the quantity changing?” How is the notion of instantaneous velocity connected to average velocity?Ĭalculus can be viewed broadly as the study of change. How do we interpret the average velocity of an object geometrically on the graph of its position function? How is the average velocity of a moving object connected to the values of its position function? Section 1.1 How do we measure velocity? Motivating Questions
Physics Applications: Work, Force, and Pressure.Using Definite Integrals to Find Volume.Cmpv (2RT/M) A value of the most probable velocity may be calculated from the values of R, T, and M. Maxwell showed that the most probable velocity is given by the expression. Using Definite Integrals to Find Area and Length velocity Most probable velocity is the velocity possessed by the largest number of molecules in a gas.Other Options for Finding Algebraic Antiderivatives.The Second Fundamental Theorem of Calculus.Constructing Accurate Graphs of Antiderivatives.Determining distance traveled from velocity.Using derivatives to describe families of functions.Using derivatives to identify extreme values.Derivatives of Functions Given Implicitly.Derivatives of other trigonometric functions.
Limits, Continuity, and Differentiability.Interpreting, estimating, and using the derivative.The derivative of a function at a point.
0 kommentar(er)
