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Instantaneous Rate of Change
Calculus The Derivative
How to estimate the instantaneous rate liquid is pouring out of a container at t=4 by computing average rates of change over shorter and shorter intervals of time.
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Average Rate of Change
Calculus The Derivative
How to compute the average rate of change of a population over an interval of time.
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Optimization Problems: Applications to Economics
Calculus Applications of the Derivative
How to use the optimization methods of calculus to optimize cost or revenue.
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The Definition of the Derivative
Calculus The Derivative
How to define the derivative of a function at a point x=a.
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Definite Integrals and Area
Calculus The Definite Integral
How to use definite integrals to find the area between a curve or under a curve.
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Position, Velocity and Acceleration
Calculus Antiderivatives and Differential Equations
How to solve position, velocity and acceleration problems using differentiation equations.
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Economics: Cost & Revenue
Calculus Applications of the Derivative
How to compute the average rate of change of the amount of a drug in a patient's bloodstream over an interval of time, and how to interpret whether the amount is increasing or decreasing over time.
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Definite Integrals As Net Change
Calculus The Definite Integral
How to use the fundamental theorem of calculus to compute the net change of a quantity.
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