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TAYLOR AND MACLAURIN

TAYLOR AND MACLAURIN. how to represent certain types of functions as sums of power series. You might wonder why we would ever want to express a known function as a sum of infinitely many terms. Integration. (Easy to integrate polynomials) Finding limit

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TAYLOR AND MACLAURIN

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  1. TAYLOR AND MACLAURIN • how to represent certain types of functions as sums of power series • You might wonder why we would ever want to express a known function as a sum of infinitely many terms. • Integration. (Easy to integrate polynomials) • Finding limit • Finding a sum of a series (not only geometric, telescoping)

  2. TAYLOR AND MACLAURIN Example: Maclaurin series ( center is 0 ) Example: Find Maclaurin series

  3. TAYLOR AND MACLAURIN Important Maclaurin Series and Their Radii of Convergence MEMORIZE: these Maclaurin Series

  4. TAYLOR AND MACLAURIN Maclaurin series ( center is 0 ) Example: Find Maclaurin series

  5. TAYLOR AND MACLAURIN TERM-081

  6. TAYLOR AND MACLAURIN TERM-091

  7. TAYLOR AND MACLAURIN TERM-101

  8. : TAYLOR AND MACLAURIN TERM-082

  9. Sec 11.9 & 11.10: TAYLOR AND MACLAURIN TERM-102

  10. Sec 11.9 & 11.10: TAYLOR AND MACLAURIN TERM-091

  11. TAYLOR AND MACLAURIN Maclaurin series ( center is 0 ) Example: Find the sum of the series

  12. TAYLOR AND MACLAURIN TERM-102

  13. TAYLOR AND MACLAURIN TERM-082

  14. TAYLOR AND MACLAURIN Example: Find the sum Leibniz’s formula:

  15. TAYLOR AND MACLAURIN Important Maclaurin Series and Their Radii of Convergence MEMORIZE: these Maclaurin Series

  16. The Binomial Series DEF: Example: Example:

  17. The Binomial Series binomial series. NOTE:

  18. The Binomial Series TERM-101 binomial series.

  19. The Binomial Series TERM-092 binomial series.

  20. TAYLOR AND MACLAURIN Important Maclaurin Series and Their Radii of Convergence Example: Find Maclaurin series

  21. TAYLOR AND MACLAURIN TERM-102

  22. TAYLOR AND MACLAURIN TERM-111

  23. TAYLOR AND MACLAURIN TERM-101

  24. TAYLOR AND MACLAURIN TERM-082

  25. TAYLOR AND MACLAURIN Important Maclaurin Series and Their Radii of Convergence MEMORIZE: these Maclaurin Series

  26. TAYLOR AND MACLAURIN Maclaurin series ( center is 0 ) Taylor series ( center is a )

  27. TAYLOR AND MACLAURIN TERM-091

  28. TAYLOR AND MACLAURIN TERM-092

  29. TAYLOR AND MACLAURIN TERM-082

  30. TAYLOR AND MACLAURIN Taylor series ( center is a ) DEF: Taylor polynomial of order n

  31. TAYLOR AND MACLAURIN The Taylor polynomial of order 3 generated by the function f(x)=ln(3+x) at a=1 is: TERM-102 DEF: Taylor polynomial of order n

  32. TAYLOR AND MACLAURIN TERM-101

  33. TAYLOR AND MACLAURIN TERM-081

  34. TAYLOR AND MACLAURIN Taylor series ( center is a ) Taylor polynomial of order n Remainder Taylor Series Taylor’s Formula Remainder consist of infinite terms for some c between a and x. REMARK: Observe that :

  35. TAYLOR AND MACLAURIN Taylor’s Formula for some c between a and x. Taylor’s Formula for some c between 0 and x.

  36. TAYLOR AND MACLAURIN Taylor series ( center is a ) DEF: nth-degree Taylor polynomial of f at a. DEF: Remainder Example:

  37. TAYLOR AND MACLAURIN TERM-092

  38. TAYLOR AND MACLAURIN TERM-081

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