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Areas Between Curves
There are times that it is necessary to add areas to find the area between the curves. The video for AP Calculus presents how to find the area between curves by subtracting the area under the lower curve from the area under the upper...
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The Second Fundamental Theorem of Calculus
How many fundamental theorems are there? The Second Fundamental Theorem of Calculus is also known as the second part of the Fundamental Theorem of Calculus. Here's a video that introduces the theorem as the method to...
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Newton's Method and Inflection Point
The inflection point, the point where the second derivative is zero, is the focus of a video that works through a problem where it is not obvious to see the roots of a function. The solution to the problem requires using...
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Volumes by Slicing
Find the volume of a rotational solid by integrating the area of a slice. The AP Calculus resource works through an example of finding the volume of a solid created by rotating a function about the x-axis. The presentation breaks the...
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Antiderivatives: Finding Position and Velocity
This AP Calculus resource works through an example that shows how to find the velocity function and the position function given acceleration. It concludes by covering how to use them to solve problems.
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The Mean Value Theorem
AP Calculus students examine the procedure for determining if the Mean Value Theorem applies to a given function. with a video that discusses the requirements needed. The instructor approaches the problem from both a graphical...
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Absolute Maximum and Minimum Values of a Function
Viewers explore the meaning of absolute maximum and minimum values for a trigonometric function within a given interval with a video that shows how to determine the critical values within the interval.The instructor then explains how to...
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Finding Limit Using L'Hospital's Rule
Apply L'Hospital's Rule to finding limits analytically. The video instructor demonstrates how to determine the limit of two different examples. Each uses the L'Hospital's Rule, but through a different application.
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Local Maximum and Minimum
AP Calculus classes follow along as a video tutorial explains the process of determining the location of local maximum and minimum. The instructor first finds the derivative using the Quotient Rule. After finding the critical...
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Derivatives of the Trigonometric Functions
Explore the derivatives of trigonometric functions through a video tutorial. The instructor shows how to evaluate a limit as x approaches infinity of a sine function. The final answer results in a limit of one.
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Differentiation of Polynomials and Exponenital Functions
Extend pupil understanding of derivatives and tangent lines. The problem presented asks individuals to find the points on a graph that have a tangent line parallel to a given line. The instructor shows how to use the concept of a...
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Continuity
Uncover the connection between continuity and roots between a given interval with a video that explains how to approach a problem that asks if roots exist between a given interval. The instructor shows how to test the interval...
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Slopes and Curves
Investigate the rate of change of graphs at a defined point with a video that explains the concept of a tangent line and how to find the slope of this line at a given point on a curve. The narrator also makes the connection to the...
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Drawing Slope Fields
Work through an example on slope fields. In a video geared for AP Calculus, viewers watch as an instructor uses a slope field generator to produce a slope field and draws particular solutions for a given differential equation.