Answer to Question #143377 in Quantitative Methods for Usman

Question #143377
Solve by iteration method:
(i) sinx = x+1/x-1
1
Expert's answer
2020-11-10T19:49:43-0500
"(x-1)\\sin x=x+1"

"x=g(x)=-\\dfrac{1+\\sin x}{1-\\sin x}"

"x_0=-0.4"


"x_{i+1}=g(x_i)=-\\dfrac{1+\\sin x_i}{1-\\sin x_i}, i=0, 1,2,..."

"\\def\\arraystretch{1.5}\n \\begin{array}{c:c:c}\n i & x_i & g(x_i) \\\\ \\hline\n 0 & -0.4 & -0.43405335 \\\\\n 1 &-0.43405335 & -0.40790368 \\\\\n 2 &-0.40790368 & -0.43196121 \\\\\n 3 & -0.43196121 & -0.40978834\\\\\n 4 & -0.40978834 & -0.43019040 \\\\\n 5 & -0.43019040 & -0.41138892\\\\\n 6 & -0.41138892 & -0.42869108\\\\\n 7 & -0.42869108 & -0.41274796\\\\\n 8 & -0.41274796 & -0.42742130\\\\\n 9 & -0.42742130 & -0.41390172\\\\\n10 & -0.41390172 & -0.42634568\\\\\n11 & -0.42634568 & -0.41488107\\\\\n12 & -0.41488107 & -0.42543436\\\\\n13 & -0.42543436 & -0.41571225\\\\\n14 & -0.41571225 & -0.42466214\\\\\n15 & -0.42466214 & -0.41641760\\\\\n16 & -0.41641760 & -0.42400769\\\\\n17 & -0.42400769 & -0.41701612\\\\\n18 & -0.41701612 & -0.42345300\\\\\n19 & -0.42345300 & -0.41752394\\\\\n20 & -0.41752394 & -0.42298282\\\\\n21 & -0.41752394 & -0.42298282\\\\\n22 & -0.42298282 & -0.41795478\\\\\n23 &-0.41795478 & -0.42258425\\\\\n24 & -0.42258425 & -0.41832028\\\\\n25 & -0.41832028 & -0.42224635\\\\\n26 & -0.42224635 & -0.41863034\\\\\n27 & -0.41863034 & -0.42195987\\\\\n28 & -0.42195987 & -0.41889336\\\\\n29 & -0.41889336 & -0.42171698\\\\\n30 & -0.42171698 & -0.41911646\\\\\n31 & -0.41911646 & -0.42151104\\\\\n32 & -0.42151104 & -0.41930569\\\\\n33 & -0.41930569 & -0.42133643\\\\\n34& -0.42133643 & -0.41946619\\\\\n35 & -0.41946619 & -0.42118838\\\\\n36 & -0.42118838 & -0.41960232\\\\\n37 & -0.41960232 & -0.42106283\\\\\n38 & -0.42106283 & -0.41971778\\\\\n39 & -0.41971778 & -0.42095638\\\\\n40 & -0.42095638 & -0.41981570\\\\\n41 &-0.41981570 & -0.42086611\\\\\n42 &-0.42086611 & -0.41989875\\\\\n43 & -0.41989875 & -0.42078956\\\\\n44 & -0.42078956 & -0.41996919\\\\\n45 & -0.41996919 & -0.42072364\\\\\n46 & -0.42072364 & -0.42002985\\\\\n47 & -0.42002985 & -0.42066875\\\\\n48 & -0.42066875 & -0.42008037\\\\\n49 & -0.42008037 & -0.42062220\\\\\n 50 &-0.42062220 & -0.42012322\\\\\n51 & -0.42012322 & -0.42058272\\\\\n52 &-0.42058272 & -0.42015956\\\\\n53 &-0.42015956 & -0.42054924\\\\\n54 & -0.42054924 & -0.42019038\\\\\n55 &-0.42019038 & -0.42052085\\\\\n56 &-0.42052085 & -0.42021652\\\\\n57 &-0.42021652 & -0.42049677\\\\\n58 &-0.42049677 & -0.42023869\\\\\n59 &-0.42023869 & -0.42047635\\\\\n\\hdashline\n60 &-0.42047635 & -0.42025749\\\\\n\\end{array}"

"x\\approx-0.4204"



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