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Calc 1
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Gravity
Terms in this set (19)
Tangent line; slope; given position, find velocity; given total change, find rate of change
Trigger words and phrases for derivatives
area; given velocity, find position; given rate of change, find total change
Trigger words and phrases for integrals
televisions per grasshoppers
Units for derivatives if f(x) is measured in televisions and x is measured in grasshoppers
televisions-grasshoppers
Units for integrals if f(x) is measured in televisions and x is measured in grasshoppers
The problems of tangent lines to curves and calculating areas under curves and inverse processes to each other
Informal geometric version of the Fundamental theorem of Calculus
Linear
What model do you use when the data points seem to be arranged more or less in a straight line
Polynomial
What model do you use when the data points seem to up and down
Power
What model do you use when the data points seem to approach 0 in one direction and there seems to be a vertical asymptote? (Cobb-Douglas product, Kepler's Third Law, Newton's Law of Gravitation)
Exponential
What model do you use when the data seems to approach 0 in one direction and there does not seem to be a vertical asymptote? (growth of money or bacteria, radioactive decay, or the heating and cooling of an object)
Logarithmic
What model do you use when the data points seem no to have a horizontal asymptote but there does seem to be a vertical asymptote? (The Richter, decibel, and pH scales)
Logistic
What type of model do you use when there seem to be two horizontal asymptotes, one to the left and one to the right? (human population size in a limited space, or transmission of an illness within a population)
Natural numbers
These are simple;they express quantities of things in front of us
Integers
These are created from the natural numbers by subtracting natural numbers
Rational Numbers
These are created from the integers by dividing integers
Real Numbers
These are created from sequences of rational numbers by virtue of the Completeness Axiom
Complex numbers
athere are created from the real numbers when we "throw in" the square root of -1.
Every sequence of rational numbers that has a [rational] ceiling also has a SMALLEST celing
State the Completeness axiom
If we start with a function f and define a new function based on integrals of f, then the derivative of the new function is the original f
More precise version of the fundamental theorem of Calculus
The rate of change of an exponential function is directly proportional to the function's (current) value
What is the feature of exponential functions that makes them so useful in applications?
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