Chapter 11
The goal of Chapter 11.
What is to find an instantaneous speed function that is good for any value of t ?
The ancient and ongoing problem that calculus helps us address.
What is the problem of change?
The three central concepts of calculus.
What are the limit of a function, the derivative of a function, and the integral of a function?
Something that is clearly physically real but seems mathematically incoherent.
What is the paradox of speed?
The job of a variable.
What is to stand for or represent things that change?
A falling cat, a falling anvil, and a falling person.
For what does Galileo's law of fall work?
The Platonic-Pythagorean project.
What is to describe the universe mathematically?
The law that ties the three central concepts together.
According to conventional notation, the input of the function f(x) is x and the output is ________.
What is f(x) ?
The formula for this sentence: The distance that a dropped object falls is equal to sixteen multiplied by the square of the time it takes to fall.
What is d = 16t2 ?
To get to the function of v(t) we use this.
What is the Method of Increments?
We use vave to represent average velocity, so how do we represent instantaneous speed?
What is v ?
The main goal of Chapter 9.
What is to apply the tool of limits to the concept of speed to arrive at a coherent definition of instantaneous speed?
Limit = the value you approach ____________.
What is "but never reach"?
What does it meant to quantify a property?
What is to represent a physical property with numbers?
Two functions we have that relate to objects falling near the earth's surface.
What are d(t) = 16t2 and v(t) = 32t ?
The i and f in ti , tf , di , and df represent these.
What are initial and final?
The question Thales was trying to answer.
What is to explain why there is both change and order in the world?
The difference between the limit of a function and the value of a function.
What is "approach" and "equal to"?
With respect to velocity, these two things are changing.
What are distance and time?
Why someone might say that the universe is "user-friendly".
What is that we are able to manipulate symbols and numbers to arrive a knowledge of the physical world which is an amazing coincidence?
The procedure used in Chapter 10 to find instantaneous speed.
What is Method of Increments?
Speed is always changing or not constant.
True or False? A function can have a limit and a value at the same point simultaneously.
What is True?
This is a mathematical system that combines algebraic formulas with pictures in Cartesian coordinates.
What is analytic geometry?