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Math 149 Lab 4 Exercises

# Math 149 Lab 4 Exercises - h x = 17 16 2 x 2 x 4 This...

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Math 149 Lab 4 - Exercises Name: < your name goes here > Section: < your section number goes here > Exercises ü Exercise 1 Consider the equation x 2 + sin( x) = 0 Use Newton's method to approximate the non-zero root accurate to ten decimal places. Start with the initial approximation x 0 = 2 and display a list of all of the approximations x 0 , x 1 , x 2, , x k which Mathematica calculates. ü Exercise 2 The tangent function y = tan x has a zero at x = p . Use Newton's method to obtain the value of p to 100 significant digits of accuracy by starting with x 0 = 3. ü Exercise 3 Consider the function
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Unformatted text preview: h ( x ) = 17 16 2 x 2 x 4 . This function has two real zeros. One is at x = r , where r is between 0 and 2, and the other root is at x = r (since h is an even function). (a) Plot a graph of the function h ( x ) on the interval [ 2 , 2 ]. (b) Write in complete sentences an explanation why Newton’s methods fails if x = 0.5 is used an an initial approximation to the root r . (c) Estimate the root r to eight places of accuracy, by starting with x 1 = 2. Mathematica...
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