This notebook demonstrates the process of moving a couch around an “L” corner so you find the longest couch that can make it around. In the picture below you can see the area function (on bottom) beginning to decrease as in the top graph we are picking up negative area.ĭownload this or other of my Calculus 1 notebooks from Google Drive Moving a Couch Around a Corner
The areas under the graph of the original function are shaded with positive area being blue and negative area being red.
This is a key idea behind the Fundamental Theorem of Calculus. This notebook lets you graph an “area function” from calculus – that is, the graph of the signed area underneath a function y= f(x) from a starting point x= a. This notebook lets you look at volumes of revolution – you can spin the region bounded by two curves around either the x-axis or y-axis.ĭownload this or other of my Calculus 1 notebooks from Google Drive Area Functions The manipulation then creates an approximation of the solid in 3D and computes the volume.ĭownload this or other of my Calculus 1 notebooks from Google Drive Volumes of Revolution You pick the curves that form the “base” of the solid as well as the type of cross-sections (triangular, circular, etc.). This notebook lets you explore the idea of finding volumes by cross-sections. This notebook lets you explore the notion that the area under the curve can be found by approximating the region with rectangles and letting that area estimate get better and better by using more and more rectangles.ĭownload this or other of my Calculus 1 notebooks from Google Drive Volumes by Cross Sections It lets you slide the tangent line along the graph of the original function and watch the graph of the derivative be constructed on the right.ĭownload this or other of my Calculus 1 notebooks from Google Drive Estimating Signed Areas by Riemann Sums This notebook lets you explore the notion of the derivative as a function. This notebook lets you explore the definition and way to estimate arc length of a curve by adding the lengths of straight line segments.ĭownload this or other of my Calculus 1 notebooks from Google Drive Estimating The Graph of the Derivative
For the limit to exist no matter how narrow you make the gap between the horizontal red lines, you should be able to force the blue-shaded portion of the curve to be between them if you make the vertical blue lines sufficiently close together.ĭownload this or other of my Calculus 1 notebooks from Google Drive Estimating Arclength This notebook has a manipulation which lets you explore the ε-δ definition of limits.
Important Note: The links for the notebooks open a new window or tab with a Google Drive page – the current settings for our homepages won’t allow me to host mathematica notebooks locally.
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