Newton's Method for Approximating Roots
Learn how Newton's Method uses tangent lines to approximate roots of functions efficiently. Explore its application and practice with exercises. Use TI Calculator and Spreadsheet for hands-on experience.
Newton's Method for Approximating Roots
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Presentation Transcript
Newton's Method Lesson 3.8
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
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
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
Example • Given • Use to approximate the root • Continue the process until the approximations differ by less than .001 • Use Calculator
Using the TI Calculator • Create a function called newt(n) • Assumes existence of f(x)
Newton's Failure • Remember that we said that usually we get a better estimate each time • Consider • Try it with your calculator
Newton's Method Spreadsheet • We will create a spreadsheet which demonstrates this concept
Assignment • Lesson 3.8 • Page 195 • Exercises 1 – 21 EOO, 29, 41
