taylor series .pdf

# In exercises 14 evaluate and at the given value 1 2 3

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In Exercises 1–4, evaluate and at the given -value. 1. 2. 3. 4. In Exercises 5–8, solve for 5. 6. 7. 8. In Exercises 9 and 10, find the point(s) of intersection of the graphs of the two equations. 9. 10. y x 1 y x 2 , y 2 x 1 y x 2 x 2, 2 x 7 0.01 2 x 3 0.01 4 5 x 0.01 x 5 0.1 x . x 1.4 f x e x 2 7 x 3, x 0.35 f x e 2 x 2, x 0.6 f x x 3 2 x 2 1, x 2.4 f x x 2 2 x 1, x f f 1148 CHAPTER 15 Series and Taylor Polynomials Skills Review 15.8 In Exercises 1 and 2, complete two iterations of Newton’s Method for the function using the given initial estimate. 1. 2. In Exercises 3–12, approximate the indicated zero(s) of the function. Use Newton’s Method, continuing until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 4 2 1 2 1 2 x y 27 54 81 6 3 3 6 27 x y y x 3 x 2 3 f x x 3 27 x 27 3 2 1 2 1 2 x y 1 1 1 x y y x 4 x 3 1 f x e x 2 x 2 1 1 2 1 2 y x 1 2 1 1 x y y e 3 x 3 x 1 f x ln x x 2 1 1 3 2 1 x y 3 2 1 3 2 1 x y f x ln x 1 x y 5 x 1 2 x 1 1 1 1 x y 1 1 1 1 x y f x x 5 x 1 f x x 3 x 1 x 1 1 f x 2 x 2 3, x 1 1.7 f x x 2 3, Exercises 15.8 See for worked-out solutions to odd-numbered exercises.

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SECTION 15.8 Newton’s Method 1149 In Exercises 13–16, approximate, to three decimal places, the x -value of the point of intersection of the graphs. 13. 14. 15. 16. In Exercises 17–30, use a graphing utility to approxi- mate all the real zeros of the function by Newton’s Method. Graph the function to make the initial estimate of a zero. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. In Exercises 31–34, apply Newton’s Method using the indicated initial estimate. Then explain why the

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