Teaching Calculus with Geogebra.pptx
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This document discusses using GeoGebra to teach key calculus concepts like limits, continuity, differentiation, and integration: - Limits can be visualized using a rotating regular polygon to show the relationship between its number of sides n and a circle. - Continuity can be explored by drawing piecewise functions and moving points on the graph. - The derivative and its definition using slopes can be demonstrated by constructing line segments, points, and slopes on functions. - Integrals are represented using Riemann sums - the upper and lower sums are calculated and compared as the number of subintervals n is changed using a slider.
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Teaching Calculus with Geogebra.pptx
- 1. Teaching Calculus with Geogebra Kapil Pundir, PGT Maths K.V. Loktak, Manipur 8077291675
- 2. Limits Continuity Differentiations Integrals
- 3. Limits • Make slider 𝑛 with minimum limit 1, maximum limit 20 and increament 1 • Make a circle with centre at origin • Make a point on positive X axis side of circle (point A) • Select tool “Rotate with given angle” and put angle 360 𝑛 𝑜 • We will get point B • Not select too “regular polygon” a selct the points A and point B • Then put the value of number of vertices as 𝑛
- 4. Piecewise function • IF 𝑥 ≤ 𝑎, 𝑓 𝑥 , 𝑎 ≤ 𝑥 ≤ 𝑏, 𝑔 𝑥 , 𝑥 ≥ 𝑏, ℎ 𝑥
- 5. Continuity • Draw piece wise function • Make a point on graph • And move the point
- 7. Derivative • Make a function f(x) • Make two points A and B on function • Make slope on point A from tools menu • In algebra view, (x(A),x(B)) (this will give point C) • Make line segments AB,AB,BC • In Algebra view, write (x(A),0), 𝑥 𝐵 , 0 , 0, 𝑦 𝐴 , 0, 𝑦 𝐵 • This will Give Points, D,E,F,G • Join segments DE, FG • Make slope on point B from tools menu • Move point A
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- 9. Kapil Pundir, PGT Maths K.V. Loktak, Manipur 8077291675