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Calculus 4E Ch 7
Calculus 4E Ch 7 - The Essential Tools: Variables, Functions, & Graphs
| Question | Answer |
|---|---|
| A variable stands for or represents things that ________________. | change |
| "The distance that a dropped object falls is equal to 16 multiplied by the square of the time it takes to fall" is represented by the formula | d=16t^2 |
| The variables "d" and "t" most directly represent ________________. They ALSO stand for distance and time. | numbers |
| There is a close connection between mathematical objects (numbers) and _________________ ones (distance and time). | physical |
| The connection between numbers & the physical world gave the Pythagoreans & Plato the idea that the cosmos is fundamentally ______________________ in the first place. | mathematical |
| quantify | to represent a physical property with numbers |
| We can quantify things like | space, time, mass, velocity, acceleration, density, force, are, and volume. |
| We cannot seem to quantify things like | color, pain, beauty, love, hunger, thirst, good, and evil. |
| INTERPRETATION is important to math because the symbols need to have __________________ attached to them to convey anything meaningful. | meanings |
| Math _______________ by giving us the tools to see how quantities of physical objects will _______________ w/o actually dealing w/ the physical objects themselves. | predicts; change |
| Velocity has to do with how much ______________ changes as ____________ changes. | distance; time |
| Acceleration has to do with how much _______________ changes as ___________ changes. | velocity; time |
| A FUNCTION is a relationship between ___________________. | variables |
| The function "d=16t^2" relates DISTANCE and TIME for a _______________ object. | falling |
| A GRAPH is a picture of a ______________; it SHOWS how variables behave together. | function |
| A ___________________ plane is like a number line on steroids. It is 2 number lines combined, a 2 dimensional number plane. | Cartesian |
| A FUNCTION can be represented as a ______________ or on a __________________. | formula; graph |
| The benefit of FORMULAS is that they allow us to _________________ calculate NUMERICAL values. | precisely |
| The benefit of GRAPHS is that they allow us to _________________ the relationship between VARIABLES. | picture |
| a mathematical system that combines ALGEBRAIC formulas with PICTURES in Cartesian coordinates; algebraic representation of shapes & the geometric representation of algebraic formulas | analytic geometry |
| "x" typically represents the ________________ variable. | independent (or input) |
| "y" typically represents the ________________ variable. | dependent (because it is dependent on the value of x) |
| "d" can also be written as "d(t)" because distance is a function of _______________. | time |
| The 3 main concepts of calculus are: | 1) the limit of a function; 2) the derivative of a function; 3) the integral of a function |
| The fundamental theorem of calculus tells us that the 3 main concepts of calculus are all _______________. | related |
Created by:
MrsHough
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