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Calculus with GeoGebra

Page history last edited by LFS 11 years, 8 months ago

Home > Teaching ToolsGeoGebra > Calculus with GeoGebra


 

Calculus with GeoGebra - Step-by-Step Students Learn Calculus with GeoGebra


      GeoGebra-Math247    (Links to all GeoGebra resources on this site.)       Calculus at Math247


New: November 2009 - 5. Riemann Sums with MadMath  and   6. Limits - Continuous functions, ε, δ


1. Boat-Landing Problem

This cool problem can be explored in 8-10th grade (see Learn and Use GeoGebra) and then solved mathematically in calculus!

Problem setting: A man with a boat at point S at sea wants to get to point Q inland. Point S is distance d1 from the closest point P on the shore, point Q is distance d2 from the closest point T on the shore and point P and T are at a distance of d.

Question: If the man rows with a speed of vr and walks with a speed of vw at what point R should he beach the boat in order to get from point S to point Q in the least possible time?

 



2. Function, Derivatives and Tangent Lines

Learning: Dynamically change the point on the function where the tangent line is drawn. Then change the function and the interval.

 



 3. Visualizing the Derivative Formula


Learning: Use GeoGebra and Algebra to Visualize and Apply the Derivative forumla

Mathcast by Prof. Dani Novak, Ph.D., Ithaca College

 


4. Related Rates - Build your own simulator
Problem: At noon, ship A is 90 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 2:00 PM?

 

5. Riemann Sums - Own the Mathematics with MadMath
Scenario: A student of beginning calculus looks at these formulas.

Formula       Formula      Formula

She says to herself - “More i’s than a fly. I can just have my calculator do this.

But her teacher is MadMath who wants her to understand what is happening and tells her to make up a GeoGebra worksheet to show and do the calculations. She knows MadMath can change the function, change the interval and change the number of subintervals so she must be prepared.

 

 

6. Limits - Continuous functions, ε, δ
Scenario: A student reads - A function f(x) is continuous at a if f(a)exists and for every ε>0, there exists δ>0 such that ...

      He says to himself - “It's all greek to me. Who can tell what this means?"

  • Try the worksheet!
  • hopefully more coming soon...
  • Keywords: limits, continuous functions, epsilon, delta, geogebra
Idea by D. Mailoino
GeoGebra Menus
  - Lists of open menus wiith tool-icon and commands positions

         in a handy two-page handout - pdf format.
 

   


Math247 GeoGebra (links to all GeoGebra resources on this site)   Got something special you want to see or show?  Contact me. Site Meter

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