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Postal Reference Code: 94110
Latitude: 37.7506
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Summarized Content

Happy New Year ! A few more links to posts on accu*ulation. Painting a Point (2-4-2013) Paint often and the paint accu*ulates. Good Question 6: 2000 AB 4 (8-25-2015) Accu*ulation Good Question 8 – or not? (1-5-2016) Accu*ulation Density (1-10-2017) Accu*ulation and Differential Equations  (2-1-2013) Solving differential equations without the “+C“  Review Notes: Type 1 Questions:… The idea that the definite integral is an “accu*ulator” means that integrating a rate of change over an integral gives the net amount of change over the interval.Many of the application of integration are based on this idea. Here are some past posts on this idea. Accu*ulation An introductory activity to explore accu*ulation and the relationship… One of the major applications of integration is to find the volumes of various solid figures. Volume of Solids with Regular Cross-sections  This is where to start with volume problems. After all, solids of revolution are just a special case of solids with regular cross-sections. Volumes of Revolution Subtract the Hole from the Whole and… So, you’ve finally proven the Fundamental Theorem of Calculus and have written on the board: And the students ask, “What good is that?” and “When are we ever going to use that?” Here’s your answer. There are two very important uses of this theorem. First, in Usually the first application of integration is to find the area bounded by a function and the x-axis, followed by finding the area between two functions. We begin with these problems First some calculator hints Graphing Integrals using a graphing calculator to graph functions defined by integrals Graphing Calculator Use  and Definition Integrals – Exam… I had an email last week from a teacher asking, how come I can use a substitution to find a power series for  , and for  , but not for  ? The answer is that you can. Substituting (2x) in to the cosine’s series give you a Taylor series centered at x = 0, a…


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/thru-the-year/topics/:
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Topics | Teaching Calculus

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Before Calculus  Limits and Continuity Differential Calculus Linear Motion Integral Calculus  Differential Equations Parametric, Vector, and Polar Equations Sequence and Series Reviewing for the AP Calculus Exams

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Teaching Calculus

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… a blog for high school calculus teachers and students

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/thru-the-year/topics/before-calculus/:
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Before Calculus | Teaching Calculus

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These are post about topics that students usually study before studying calculus. Some go back to Algebra 1 or earlier. You may want to share these ideas with the teachers of the courses that come before your calculus course. Teaching How to Read Mathematics (4-12-2013) Some suggestions on reading textbooks The Unknown Thing (8-10-2012) A…

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Teaching Calculus

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… a blog for high school calculus teachers and students

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/thru-the-year/topics/limits-and-continuity/:
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Limits and Continuity | Teaching Calculus

Description

CONTINUITY To help understand limits it is a good idea to look at functions that are not continuous. Historically and practically, continuity should come before limits. On the other hand, the definition of continuity requires knowing about limits. So, I list continuity first. The modern definition of limit was part of Weierstr ' definition of continuity.  Continuity (8-13-2012)…

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/thru-the-year/topics/differential-calculus/:
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Differential Calculus | Teaching Calculus

Description

Below are the post on differential calculus, derivatives, and their applications. Scroll down or use these links to take you directly to the various sections: DEFINITION OF THE DERIVATIVE FINDING DERIVATIVES APPLICATIONS: THE MEAN VALUE THEOREM (MVT) APPLICATIONS: GRAPHING AND EXTREME VALUES OTHER APPLICATIONS OF DERIVATIVES REVIEW NOTES _____ DEFINITION OF THE DERIVATIVE Local Linearity…

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… a blog for high school calculus teachers and students

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/thru-the-year/topics/6921-2/:
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Linear Motion | Teaching Calculus

Description

LINEAR MOTION PROBLEMS (AB AND BC CALCULUS) Linear motion is an application of both derivatives and integrals that appears on the AP Calculus exams for both AB and BC. Motion in a plane governed by parametric equations and vectors is a BC only topic. See the Parametric, Vector and Polar Equations page. The Ubiquitous Particle Motion…

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