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Calculus Course

Calculus Course. ~. X-Ray. Original. Rings. Slices. Boards. Ring By Ring Timelapse. 25%. 50%. 75%. 100%. X-Ray. Shape. X-Ray View. Step-by-step. X-Ray Shape. Step-by-step. 2*pi*r. dr. r. r. p. dp. dx. x. 2*pi*r. dr. r. r. p. dp. dx. x. Shape Animation Spin.

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Calculus Course

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  1. Calculus Course

  2. ~

  3. X-Ray Original Rings Slices Boards

  4. Ring By Ring Timelapse 25% 50% 75% 100%

  5. X-Ray

  6. Shape

  7. X-Ray View Step-by-step

  8. X-Ray Shape Step-by-step

  9. 2*pi*r dr r r p dp dx x

  10. 2*pi*r dr r r p dp dx x

  11. Shape Animation Spin

  12. Start with a ring Build out a disc Combine discs into a sphere Subtract a smaller sphere to get a “Shell”

  13. Circle Rings Slices Boards Sphere Shells Wedges Plates

  14. ? Circumference Area Volume Surface area Ring-by-ringTimelapse Plate-by-plateTimelapse Shell-by-ShellX-Ray

  15. Take a Ring Ring-by-ring timelapse… to a circle Plate-by-plate timelapse… to a sphere Shell-by-Shell X-Ray… to surface area Take a sphere

  16. = + = • 2 ×

  17. No • Aha! Yes

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