Names:Date:Solving the initial value problem 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 numerically for two problems on the interval LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYHhfXzBgRictSSNtb0dGJDYtUSYmbGVxO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRidGLy1GLDYjUSdgeF9fZmBGJ0Yz , to get an approximate value of 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1.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Only re-execute the following code repeatedly, changing the value of N through the values 0,1,2,3,... by trial and error until you get exactly what you want. The value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the number of times you halve the initial interval division of 50. The additional looping is for your convenience so you don't have to execute this repeatedly for each new value of the stepsize.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[Notice that rounding off "LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjX3lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn" we want to get 3.437 twice in a row after rounding to 3 decimal places for this example ("LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoeV9leGFjdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=" rounded to 3 decimal places), so that explains where we stopped here at 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: this is different than just getting the first 3 decimal places correct, which occurs already at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJjEyODAwRidGOUY5, when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjhGJ0Y5Rjk=.]
[Put your final comment here, like: "We had to double the number of steps 11 times to get the correct 3 decimal place answer after rounding off, twice in a row." Also put in the answer to the error halving question: roughly by what factor does the error decrease each time you half the stepsize? Look at the successive "_error" results to draw your conclusion.
When you are done, delete all this extra stuff in brackets, please.]2.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Only re-execute the following code repeatedly, changing the value of N through the values 0,1,2,3,... by trial and error until you get exactly what you want. The value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the number of times you halve the initial interval division of 50. The additional looping is for your convenience so you don't have to execute this repeatedly for each new value of the stepsize.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[Notice that rounding off "LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjX3lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn" we want to get 3.437 twice in a row after rounding to 3 decimal places for this example ("LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoeV9leGFjdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=" rounded to 3 decimal places), so that explains where we stopped here at 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: this is different than just getting the first 3 decimal places correct, which occurs already at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJjEyODAwRidGOUY5, when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjhGJ0Y5Rjk=.]
[Put your final comment here, like: "We had to double the number of steps 11 times to get the correct 3 decimal place answer after rounding off, twice in a row." Also put in the answer to the error halving question: roughly by what factor does the error decrease each time you half the stepsize? Look at the successive "_error" results to draw your conclusion.
When you are done, delete all this extra stuff in brackets, please.]LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMvJStleGVjdXRhYmxlR0Y0Ri8=