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Taylor Series

Taylor Series

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Taylor Series

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  1. Taylor Series

  2. Theorem

  3. Definition The series is called the Taylor series of f about c (centered at c)

  4. Definition The series is called the Maclaurin series of f about c (centered at c) Thus a Maclaurin series is a Taylor series centered at 0

  5. Examples I

  6. Example (1)Taylor Series for f(x) = sinx about x = 2π

  7. Taylor Series for sinx about 2π

  8. Example (2)Taylor Series for f(x) = sinx about x = π

  9. Taylor Series for sinx about π

  10. Example (3)Taylor Series for f(x) = sinx about x = π/2

  11. Taylor Series for sinx about π/2

  12. Example (4)Maclaurin Series for f(x) = sinx

  13. Maclaurin Series for sinx

  14. Example(5)The Maclaurin Series for f(x) = x sinx

  15. Examples II

  16. Example (1)Maclaurin Series for f(x) = ex

  17. Maclaurin Series for ex

  18. Example (2) Find a power series for the function g(x) =

  19. Example (3)TaylorSeries for f(x) = lnx about x=1

  20. Taylor Series for lnx about x = 1

  21. I-1Taylor Series for f(x) = cos2x about x = 5π

  22. Taylor Series for cos2x about 5π

  23. I-2Taylor Series for f(x) = cosx about x = 3π/4

  24. Taylor Series for cosx about 3π/4

  25. I.3Taylor Series for f(x) = cosx about x = π/6

  26. Taylor Series for cosx about π/6

  27. I.4Taylor Series for f(x) = e3x about x = 5

  28. Homework