Please look at all the numbers 1-9
Guided Project 12 of it to approximate solutions to equations of the ke all approximation methods,Newton's method does thancti Lithis project, you will see the simple idea based on disegs à few pitfalls of Newton's method. Topics and skills: Derivaave Many software packages use differe form to) O where fis ai this tangent lines that led Newton to not always work; therefore, it's als ges use Newton's method oration to cally Assume r is a solution of f)-o, which means Deriving Newton's Method ity dehpe d geom To the curve y-fx) at5 is approximation Xy.we repeat the t in a sequence netangent to the curve at x.x Newton's method is most easily de r)-O: our goal is to approxim 체 isan initial estimate of, that might have been obtained by opefully) better approximation to r, two steps are carried some preliminary analysis (Figure itersects the x-axis is found, this new estimate is calleds mation to the root r than o To improve upon the out: a line tangent to the curve y tangent line the pointx at which the (Figure 2), ' at which the tangeat line approxi Ficure 2 is a better oss using x, to determine the next estimate x (Figure 3) Figure 2 rceces f pproximations) that ideally get eloser and Continuing in this fashion, we oshe e derive a formula for finding ing in this fashion, we obtain to is usedtofi dan updated Pigure 4) In Steps ing x approximate valoe in terms of x" . Figure 2 Figure 1 Figure 4 Figure 3 Recall the point-slope form of the equation of a line of slope m passing through (xy.y) is y-s-m(x-xi). Use this equation to venty that the line tangent to the curve y = f(x) at x = s