Question APPLY FIXED-POINT ITERATION SIX TIMES WITH STARTING POINT \( X_{0}=10 \) TO FIND AN APPROXIMATED SOLUTION FOR \( x=20 \cdot \cos \left(\frac{x}{40}\right) \) THIS WILL RESULT IN a sPIRALING CONVERGENCE. DOES THIS MEAN THAT THE ANSWER IS TOO SMALL OR TOO HIGH?
RI7PDD The Asker · Advanced Mathematics
Transcribed Image Text: APPLY FIXED-POINT ITERATION SIX TIMES WITH STARTING POINT \( X_{0}=10 \) TO FIND AN APPROXIMATED SOLUTION FOR \( x=20 \cdot \cos \left(\frac{x}{40}\right) \) THIS WILL RESULT IN a sPIRALING CONVERGENCE. DOES THIS MEAN THAT THE ANSWER IS TOO SMALL OR TOO HIGH?
More Transcribed Image Text: APPLY FIXED-POINT ITERATION SIX TIMES WITH STARTING POINT \( X_{0}=10 \) TO FIND AN APPROXIMATED SOLUTION FOR \( x=20 \cdot \cos \left(\frac{x}{40}\right) \) THIS WILL RESULT IN a sPIRALING CONVERGENCE. DOES THIS MEAN THAT THE ANSWER IS TOO SMALL OR TOO HIGH?
Community Answer
NB0FML
【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/2Solution:Given: \( \mathrm{{f{{\left({x}\right)}}}={20}{\cos{{\left(\frac{{x}}{{40}}\right)}}}{\quad\text{and}\quad}{x}_{{0}}={10}} \)\( \mathrm{\Rightarrow\phi{\left({x}\right)}={20}{\cos{{\left(\frac{{x}}{{40}}\right)}}}} \)Using the Fixed Point Iteration Method,\( \mathrm{{x}_{{1}}=\phi{\left({x}_{{0}}\right)}=\phi{\left({10}\right)}={19.378}} \)\( \mathrm{{x}_{{2}}=\phi{\left({x}_{{1}}\right)}=\phi{\left({19.378}\right)}={17.699}} \)\( \mathrm{{x}_{{3}}=\phi{\left({x}_{{2}}\right)}=\phi{\left({17.699}\right)}={18.074}} \)\( \mathrm{{x}_{{4}}=\phi{\left({x}_{{3}}\ ... See the full answer