Содержание
- 2. Lecture Outline
- 3. Brief History Blaise Pascal 17th century Gave the form that we will learn today for a
- 4. Applications Binomial expansions are used in probability for predicting nation’s economy, weather forecasting, etc. (We will
- 5. Pascal’s triangle The numbers you saw in the preview activity form a triangle called Pascal’s triangle.
- 6. Did you find the pattern and the next two rows?
- 7. Binomial expansions using Pascal’s triangle
- 8. Example 1
- 9. Your turn!
- 10. Binomial expansions using combinations Can you think of any drawback of using Pascal’s triangle?
- 11. Combinations In mathematics, a combination is a selection of items from a collection where the order
- 12. Combinations Undefined
- 13. Combinations
- 15. Using the calculator to find nCr 1 5 4 3 2
- 16. Example 2 From the letters ABC, how many different ways of choosing 2 letters?
- 17. Computations of some nCr The numbers look familiar! These numbers are the numbers that we saw
- 18. Comparisons: Pascal’s triangle and Combinations This allows us to find the coefficients without drawing the Pascal’s
- 19. Binomial expansions using combinations
- 20. Example 3
- 21. Your turn!
- 22. Example 4
- 23. Solution
- 24. Your turn!
- 25. Solution
- 30. By using this expansion, we can approximate a non-polynomial function by polynomials. Polynomials are the easiest
- 31. Example 5
- 32. Solution (continued)
- 33. Your turn!
- 34. Solution
- 36. Example 6
- 37. Your turn!
- 38. Solution
- 39. Your turn!
- 40. Solution
- 41. Example 7
- 42. Solution
- 43. Learning outcomes 4.4.1. Expand binomial expressions 4.4.2. Find a particular term in binomial expansions 4.4.3. Use
- 44. Formulae
- 46. Скачать презентацию