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Calculus from the beginning

Calculus from the beginning. What is calculus?. Calculus is the study of change, it has two main branches Differential Calculus – The study of change Integral Calculus- The study of area/accumulation But they both start with a foundation in: Precalculus (Algebra, Geometry and Trig) Limits.

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Calculus from the beginning

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  1. Calculus from the beginning

  2. What is calculus? • Calculus is the study of change, it has two main branches • Differential Calculus – The study of change • Integral Calculus- The study of area/accumulation • But they both start with a foundation in: • Precalculus (Algebra, Geometry and Trig) • Limits

  3. Agenda • Speedy Review of Critical Precalculus Skills • Overview of Limitsand Continuity • Concept of a Derivative and Derivative Rules • Applications of Derivatives • Concept of the Integral • Application of the Integral

  4. PRECALCULUS DRILLS AND FACTS • Algebra • Functions • Exponents and Logs • Trigonometry Developed by Susan Cantey and student Elizabeth Albert at Walnut Hills H.S. 2006

  5. I’m going to ask you a lot of questions about math. These are facts that you should know extremely well. You also need to be able to recall them quickly if you want to succeed in Calculus. When you think you know the answer, (or if you give up ) click to get to the next slide to see if you were correct. Ready?

  6. Define an Even Function

  7. Note: It is NOT enough to know the graph is symmetric with respect to the y-axis.

  8. Define an Odd Function

  9. Again, please note that it is NOT enough to know that the graph has origin symmetry.

  10. See if you can identify the function that probably goes with each of these simple graphs….

  11. How about these?

  12. How about these?

  13. What about this one?

  14. How about these?

  15. and respectively

  16. and finally:

  17. The graph of x = a is…

  18. … a vertical line.

  19. The graph of y = a is…

  20. … a horizontal line.

  21. OK…that’s enough about graphs! Let’s move on…

  22. Think “flower” & “root”

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