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Newton's Method

Newton's Method. Lesson 3.8. Newton Views Roots. Consider a function as it crosses the x-axis (the root) Newton saw that the tangent line close to the root crossed the x-axis close to the root. Try this on Geogebra. x 1. x 2. Newton's Method.

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Newton's Method

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  1. Newton's Method Lesson 3.8

  2. Newton Views Roots • Consider a function asit crosses the x-axis (the root) • Newton saw that the tangent line close to the root crossed the x-axis close to the root Try this on Geogebra

  3. x1 x2 Newton's Method • That line intersection can be easily calculated • Let y = 0, solve for x • Use that point as a second (and usually better) estimate for the root of the function

  4. Newton's Method for Approximating Roots • Given f(x) we seek a root • If xn is an approximation for the root Then we claimis a better approximation • xn+1 x1

  5. Example • Given • Use to approximate the root • Continue the process until the approximations differ by less than .001 • Use Calculator

  6. Using the TI Calculator • Create a function called newt(n) • Assumes existence of f(x)

  7. Newton's Failure • Remember that we said that usually we get a better estimate each time • Consider • Try it with your calculator

  8. Newton's Method Spreadsheet • We will create a spreadsheet which demonstrates this concept

  9. Assignment • Lesson 3.8 • Page 195 • Exercises 1 – 21 EOO, 29, 41

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