1)While we've seen how Newton's Method can be used to approximate square roots of values, another iterative process that predates Newton's Method has also been used to approximate square roots. Let xnbe an approximation of ?m . It is a given that xnand m are both positive values. (a) If xnis close to of ?m , explain why m xn is also close to ?m . (b) Explain why the actual value of ?m lies between xnand m xn

(c) Explain why xn+1 = 12(xn+ mxn) would give a reasonable approximation of ?m . (d) Use this formula with x1 = 5 to approximate ?26 correct to at least 6 decimal places. (e) Setup the Newton's Method formula that can be used to approximate ?m and show that it gives the same formula as the process above.

2)Use the diagram below to show graphically where x2 and x3 would be if you used Newton's Method to approximate the root of y = f (x) with initial estimate x1.

Chrome File Edit View History Bookmarks Profiles Tab Window Help () 57 0 53 0 7 9 8 0 Tue Nov 8 12:23 PM .. . + Copy of WRIT 1301_Project 2 T X Week 9: Linearizations, Differe X Mi Inbox (127) - sharm882@umn.( X + of 6 ZOOM + 7. Use the diagram below to show graphically where x2 and x3 would be if you used Newton's Method to approximate the root of y = f(x) with initial estimate x1. y = f(x) 1 Page 4 Resume aayush.rtf Week9 Collision .pdf car data lab 8 -....pdf Resume aayush.pdf spring lab data -....pdf One of the challe....pdf ~ Show All Removed 130 NOV 8 stv 4 Aa