language use 28 videos
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Approximating Area Using Rectangles
Calculus The Definite Integral
How to approximate the area under a curve using rectangles.
approximating area under a curve left hand sums right hand sums limits -
Computing Definite Integrals using Substitution
Calculus The Definite Integral
How to evaluate definite integrals using the method of substitution.
definite integral the method of substitution limits of integration antiderivative -
Optimization Using the Closed Interval Method
Calculus Applications of the Derivative
How to evaluate the limit of a function at points where it is not continuous.
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Optimization Using the First Derivative Test
Calculus Applications of the Derivative
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.
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Optimization Using the Second Derivative Test
Calculus Applications of the Derivative
How to compute the average velocity of an object moving in one dimension from a graph of its position vs. time.
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Limits: A Numerical Approach
Calculus Limits and Continuity
How to estimate a limit using a table of values.
limits functions table of values numerical approach undefined -
Evaluating Limits Algebraically, Part 1
Calculus Limits and Continuity
How to evaluate the limit of a function using continuity.
limits definition of continuous function domain of a function rational functions -
Derivative Notation
Calculus The Derivative
How to recognize and use Newton's and Leibniz's notation for the derivative.
derivative newton form leibniz form differentiation the differential operator -
Intervals of Increase and Decrease
Calculus Applications of the Derivative
How to estimate a limit using a table of values.
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Curve Sketching with Derivatives
Calculus Applications of the Derivative
How to evaluate the limit of a function using continuity.
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The Method of Substitution
Calculus Antiderivatives and Differential Equations
How to evaluate an indefinite integral using the method of substitution.
antidifferentiation method of substitution change of variables derivatives differential -
The First Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to use an algebraic approach to find one-sided limits of a rational function, and how these limits can be used to find a vertical asymptote.
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One-Sided Limits
Calculus Limits and Continuity
How to use one-sided limits to show that a limit does not exist.
one sided limits two sided limits limit does not exist piecewise functions left hand limit right hand limit table of values numerical approach -
Infinite Limits; Vertical Asymptotes
Calculus Limits and Continuity
How to use one-sided limits to find a vertical asymptote.
one sided limits infinity limit does not exist rational functions left hand limit right hand limit table of values numerical approach vertical asymptote -
Derivatives of Polynomial Functions
Calculus The Derivative
How to compute the derivative of a polynomial function using two properties of the derivative.
the constant multiple rule the sum rule of derivatives polynomial functions derivative -
Derivatives of Exponential Functions
Calculus The Derivative
How to use the definition of the derivative to find a derivative formula for exponential functions.
limits derivative definition of the derivative difference quotient exponential functions natural logarithm -
Derivatives of Logarithmic Functions
Calculus The Derivative
How to infer the derivative of the natural log function using a calculator investigation.
derivative formula limits derivative the number e numerical approximation of the derivative natural logarithm -
Relative Maxima and Minima
Calculus Applications of the Derivative
How to use one-sided limits to find a vertical asymptote.
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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.
cost revenue average cost optimization methods closed interval method first derivative test second derivative test -
Indefinite Integrals
Calculus Antiderivatives and Differential Equations
How to solve an indefinite integral using the properties of indefinite integrals.
indefinite integral antiderivative antidifferentiation differentiation
