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Higher-order derivatives and power series

Higher-order derivatives and power series. ACME General Store Sales receipt. Higher-order derivatives and power series. 2 nd derivative and curvature. Power series. 1. 1/2. Power series for sine and cosine. Approximation of p. 2 nd derivative and curvature. upward slant. horizontal.

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Higher-order derivatives and power series

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  1. Higher-order derivatives and power series ACME General Store Sales receipt

  2. Higher-order derivatives and power series 2nd derivative and curvature Power series 1 1/2 Power series for sine and cosine Approximation of p

  3. 2nd derivative and curvature upward slant horizontal downward slant positive slope zero slope increasing slope negative slope positive second derivative 0 0 0

  4. Higher-order derivatives and power series 2nd derivative and curvature Power series 1 1/2 Power series for sine and cosine Approximation of p

  5. Constructing power series representations 0

  6. Constructing power series representations Multiply coefficient and powers of binomial Subtract 0 Add terms

  7. Construction of accurate power series representation can fail Too jagged 0 0 0 Too straight

  8. Higher-order derivatives and power series 2nd derivative and curvature Power series 1 1/2 Power series for sine and cosine Approximation of p

  9. Qualitative expectations for power series for sine 1 Expand around qE= 0 0 -1

  10. Power series for sine Expand around qE= 0 1

  11. Power series for sine Expand around qE= 0

  12. Power series for sine is as expected 1 0 -1

  13. Higher-order derivatives and power series 2nd derivative and curvature Power series 1 1/2 Power series for sine and cosine Approximation of p

  14. Using a power series and iteration to approximate p 1 1/2

  15. Higher-order derivatives and power series 2nd derivative and curvature Power series ACME General Store Sales receipt 1 1/2 Power series for sine and cosine Approximation of p

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