MAT1505-01/02 21F Take Home Test 3 Print Name (Last, First) _______________________________|____Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use EQUAL SIGNS and arrows when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation when appropriate). Indicate where technology is used and what type (Maple, GC). Maple may not substitute for any hand calculations unless explicitly stated, but use it to check each step if you want to be safe.pledgeWhen you have completed the exam, please read and sign the dr bob integrity pledge and hand this test sheet in on top of your answer sheets as a cover page, with the first test page facing up:"During this examination, all work has been my own. I give my word that I have not resorted to any ethically questionable means of improving my grade or anyone else's on this examination and that I have not discussed this exam with anyone other than my instructor, nor will I until after the exam period is terminated for all participants."
Signature: Date: 1. Consider the power series 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) Determine the radius of convergence and the interval of convergence including endpoints. Justify your claims.
b) Use Maple to evaluate f(4) exactly and to 5 decimal places.c) Optional. What does Maple evaluate this too, provided you assume x lies in the interval of convergence? Does its plot agree with your determination of the interval of convergence and its endpoints?
2. Use Taylor series to evaluate the limit 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. Explain your steps.
3. a) Evaluate the Taylor cubic polynomial LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRi82JVEieEYnRjJGNS8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj5GPkZORj4= for the function 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 at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjRGJ0Y5LyUrZXhlY3V0YWJsZUdGPUY5 using the definition (hand evaluation!).
b) What is the numerical value of this approximating polynomial at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjVGJ0Y5LyUrZXhlY3V0YWJsZUdGPUY5 to 5 decimal places.
c) Estimate the error in using this polynomial to approximate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYjNiQtSSNtbkdGJDYkUSI1RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjhGOA== (alternating series) and compare it with the numerical value of the exact error.
4. The formula 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 for the period of a simple pendulum we learn in high school and freshman physics only applies for small angles 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of maximum angular displacement from the downward vertical direction. A quick search of the web reveals that the exact formula has a correction factor
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,
where 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. For a pretty large swing angle of 60\302\260, note that 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.
a) Write out the first 3 nonzero terms of this series for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInhGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA=, which form the Taylor fourth degree polynomial LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2J1EiVEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGNC8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictRiM2Jy1JI21uR0YkNiRRIjRGJy9GOFEnbm9ybWFsRidGMkY1RjdGOi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLzYlUSJ4RidGNS9GOFEnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0ZDRkNGVUZD. Notice that the first term is 1 since this formula needs no correction at very small angles.b) Evaluate this numerically to 4 decimal places for an angle of 60\302\260.
c) Derive the radius of convergence R of this series representation of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInhGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA= in x using explicit limit notation. What angle LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSVtcm93R0YkNiQtSSNtbkdGJDYkUSIwRidGMkYyLyUvc3Vic2NyaXB0c2hpZnRHRjsvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJw== does this maximum value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== correspond to? Can you think of any physical reason connected to the motion of the pendulum why this angle might cause trouble?d) Maple can evaluate the sum of this infinite series for f(x) exactly for any value of x for which the series converges. What is the numerical value of the series for a 60\302\260 degree angle?e) We only need to evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInhGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA= correct to 2 decimal places to evaluate the percentage error to the nearest integer by which the exact result for T differs from the simple formula 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 for a 60\302\260 degree angle. What is this percentage error corresponding to the fractional error 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? What is the exact value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInhGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA= to 4 decimal places for a 60\302\260 degree angle?f) If you examine the list of values LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2J1EiVEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGNC8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictRiM2Ji1JI21uR0YkNiRRIjJGJy9GOFEnbm9ybWFsRictRi82JVEibkYnRjUvRjhRJ2l0YWxpY0YnRjVGSC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GQDYkUSQwLjVGJ0ZDLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGQ0ZDRlhGQw==, at what value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJuRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGOEYv does the Taylor approximation at this angle round off to the 4 decimal place value of the exact correction factor? Be sure to justify this conclusion by stating at least the 5 decimal place value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2J1EiVEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGNC8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictRiM2Ji1JI21uR0YkNiRRIjJGJy9GOFEnbm9ybWFsRictRi82JVEibkYnRjUvRjhRJ2l0YWxpY0YnRjVGSC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GQDYkUSQwLjVGJ0ZDLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGQ0ZDRlhGQw== for both LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJuRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGOEYv and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZGLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlUtRiw2JFEiMUYnRi8vJStleGVjdXRhYmxlR0ZGRi9GL0ZlbkYv.solution3. Taylor from formulaLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JUYrLUkmbXNxcnRHRiQ2Iy1GIzYkLUkjbW5HRiQ2JFEjNS5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY6LUkjbW9HRiQ2LVEifkYnRjovJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkMvJSlzdHJldGNoeUdGQy8lKnN5bW1ldHJpY0dGQy8lKGxhcmdlb3BHRkMvJS5tb3ZhYmxlbGltaXRzR0ZDLyUnYWNjZW50R0ZDLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUi8lK2V4ZWN1dGFibGVHRkNGOg==These derivatives are easy to evaluate by hand with the power rule.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We need the next term in the series to estimate the error. Since the next term is negative, this truncated value is too high. The true value is lower by a positive amount which we evaluate from the difference 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The next term after LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIzRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQUYyRkE= is negative so the exact value is smaller than T(3) at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjVGJ0Y5LyUrZXhlY3V0YWJsZUdGPUY5 but a bit less than the estimate, as it should be.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1. ln related 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 inspiraton from textbook, altered a bit.c) Optional. This represents 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
which we can get from the series expansion of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JVEjbG5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYkLUYjNigtSSNtbkdGJDYkUSIxRidGMi1JI21vR0YkNi1RIitGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGUi1GPzYtUSJ+RidGMkZCRkRGRkZIRkpGTEZOL0ZRUSYwLjBlbUYnL0ZURlktRiw2JVEieEYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGMUYyRjJGVS1GPzYtUSI9RidGMkZCRkRGRkZIRkpGTEZOL0ZRUSwwLjI3Nzc3NzhlbUYnL0ZURmJvRmVuRj4tRj82LVEjLi5GJ0YyRkJGREZGRkhGSkZMRk5GUEZaLUY/Ni1RIi5GJ0YyRkJGREZGRkhGSkZMRk5GWEZaRlVGXG9GMg==by dividiing it by x, multiplying by 5 and then substituting 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, in other words by algebra tricks.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 of the vertical asymptote at 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, the radius of convergence is 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.Absolute convergence ratio test:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY5LUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRIm5GJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RKiZjb2xvbmVxO0YnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWLUkmbWZyYWNHRiQ2KC1JJW1zdXBHRiQ2JS1GNjYkLUYjNictRiw2JVEieEYnRi9GMi1GQzYtUSgmbWludXM7RidGQEZGRkhGSkZMRk5GUEZSL0ZVUSwwLjIyMjIyMjJlbUYnL0ZYRmRvLUkjbW5HRiQ2JFEiM0YnRkBGPUZARkAtRiM2JUY6Ri9GMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRiM2Jy1GLDYjUSFGJy1GIzYmLUY2NiQtRiM2JkY6LUZDNi1RIitGJ0ZARkZGSEZKRkxGTkZQRlJGY29GZW8tRmdvNiRRIjFGJ0ZARkBGQC1GQzYtUSJ+RidGQEZGRkhGSkZMRk5GUEZSL0ZVUSYwLjBlbUYnL0ZYRmRxLUZnbjYlLUZnbzYkUSI1RidGQC1GIzYkRjpGQEZccEZARmFwRi9GMi8lLmxpbmV0aGlja25lc3NHRl9xLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmFyLyUpYmV2ZWxsZWRHRj8tRkM2LVEiO0YnRkBGRi9GSUYxRkpGTEZORlBGUkZjcUZXLUZaNigtRiM2JkYrLUY2NiQtRiM2J0Y6RmpwRl1xRj1GQEZARj1GQC1GIzYmRistRjY2JEZqb0ZARi9GMkZdckZfckZickZkckZmci1GLDYlUSlzaW1wbGlmeUYnRi9GMi1GNjYkLUYjNictRiw2JVEiJUYnRi9GMi1GQzYtUSIsRidGQEZGRmlyRkpGTEZORlBGUkZjcS9GWFEsMC4zMzMzMzMzZW1GJy1GLDYlUSlzeW1ib2xpY0YnRi9GMkY9RkBGQEZmci1JJ211bmRlckdGJDYlLUZDNi1RJGxpbUYnRkAvRkdRJnVuc2V0RicvRklGX3UvRktGX3UvRk1GX3UvRk9GX3UvRlFGMS9GU0ZfdUZjcS9GWFEsMC4xNjY2NjY3ZW1GJy1GIzYmRjotRkM2LVEtJnJpZ2h0YXJyb3c7RidGQEZGRkgvRktGMUZMRk5GUEZSRlRGVy1GQzYtUSgmaW5maW47RidGQEZGRkhGSkZMRk5GUEZSRmNxRmVxRkAvJSxhY2NlbnR1bmRlckdGPy1GNjYkLUYjNiVGXXRGPUZARkBGZnItRjY2JkZldkZALyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRlt3RmBxLUZDNi1RIjxGJ0ZARkZGSEZKRkxGTkZQRlJGVEZXRmBxRl1xRmZyLUYsNiVRJnNvbHZlRidGL0YyRmN2Rj1GQA==To evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUkjbW5HRiQ2JFEiNEYnL0YzUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj5GPkZARj4= we just plug 4 into the infinite series.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 endpoint: convergent alternating harmonic series.
Left endpoint: divergent harmonic series.
The factors of 5 cancel, leaving the obvious coefficients of these respective series: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4. pendulumSee https://en.wikipedia.org/wiki/Pendulum#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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlXXBGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiRxKEYqLSUpQ0hJTERSRU5HNiI=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The Taylor polynomial LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy1GLzYlUSJuRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTy8lKXN0cmV0Y2h5R0ZPLyUqc3ltbWV0cmljR0ZPLyUobGFyZ2VvcEdGTy8lLm1vdmFibGVsaW1pdHNHRk8vJSdhY2NlbnRHRk8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zobi1GLzYlUSNUMkYnRjJGNS1JKG1mZW5jZWRHRiQ2JC1GIzYlRkAvJStleGVjdXRhYmxlR0ZPRj5GPi1GSjYtUSI6RidGPkZNRlBGUkZURlZGWEZaRmZuRmluRmNvRj4=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEjVDJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJORidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSomY29sb25lcTtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVi1JK211bmRlcm92ZXJHRiQ2Jy1GQzYtUSYmU3VtO0YnRkAvRkdRJnVuc2V0RicvRklGam4vRktGMS9GTUZqbi9GT0YxL0ZRRjEvRlNGam4vRlVRJjAuMGVtRicvRlhRLDAuMTY2NjY2N2VtRictRiM2Ji1GLDYlUSJuRidGL0YyLUZDNi1RIj1GJ0ZARkZGSEZKRkxGTkZQRlJGVEZXLUkjbW5HRiQ2JFEiMEYnRkBGQC1GIzYnRjpGLy8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnLyUscGxhY2Vob2xkZXJHRjFGMkZSLyUsYWNjZW50dW5kZXJHRj8tRjY2JC1GIzYpLUYsNiVRIkFGJ0YvRjItRjY2JC1GIzYoRmdvRi8vRmRwUStbMCwxNjAsODBdRidGZnAvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjFGMkZARi9GZXFGZnBGZ3FGMkZALUZDNi1RIjtGJ0ZARkYvRklGMUZKRkxGTkZQRlJGYW9GV0YrLUY2NiQtRiM2JS1GXnA2JFEiM0YnRkBGPUZARkAtRkM2LVEifkYnRkBGRkZIRkpGTEZORlBGUkZhby9GWEZib0ZpcS1GLDYlUSVldmFsRidGL0YyLUY2NiQtRiM2KkYrRl1yLUZDNi1RIixGJ0ZARkZGXHJGSkZMRk5GUEZSRmFvL0ZYUSwwLjMzMzMzMzNlbUYnLUYsNiVRInhGJ0YvRjJGam8tRl5wNiRRJDAuNUYnRkBGPUZARkBGaXEtRiw2JVEmYXJyYXlGJ0YvRjItRjY2JC1GIzYlLUY2NiYtRiM2Ji1GLDYlUSRzZXFGJ0YvRjItRjY2JC1GIzYrLUY2NiYtRiM2LS1GLDYlUSJrRidGL0YyRl9zLUZecDYkUSIyRidGQEZkckZgdUZfc0ZkckZoci1GNjYkLUYjNipGKy1GNjYkLUYjNiVGYHVGPUZARkBGX3NGZHNGam9GZ3NGPUZARkBGPUZARkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGX3NGYHVGam9GXXAtRkM2LVEjLi5GJ0ZARkZGSEZKRkxGTkZQRlIvRlVRLDAuMjIyMjIyMmVtRidGZ3ItRl5wNiRRIjhGJ0ZARj1GQEZARj1GQEZARl52RmF2Rj1GQEZARj1GQA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkmbWZyYWNHRiQ2KC1GIzYqLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJ0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkwtRiM2Ki1JI21pR0YkNiVRKkVsbGlwdGljS0YnLyUnaXRhbGljR0Y9RjQtRjg2LVEwJkFwcGx5RnVuY3Rpb247RidGNEY7Rj5GQEZCRkRGRkZIRkpGTS1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYxNiRRJDAuNUYnRjQvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRicvJStleGVjdXRhYmxlR0Y9LyUpcmVhZG9ubHlHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0Y0RjRGXG9GX29GYW9GZG9GNEZcb0Zfb0Zhb0Zkb0Y0LUZSNiVRJSZwaTtGJ0ZVRjQvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl9wLyUpYmV2ZWxsZWRHRj0tRjg2LVEifkYnRjRGO0Y+RkBGQkZERkZGSEZKRk0tRjg2LVEiO0YnRjRGOy9GP0Zjb0ZARkJGREZGRkhGSi9GTlEsMC4yNzc3Nzc4ZW1GJy1GUjYlUSZldmFsZkYnL0ZWRmNvL0Y1USdpdGFsaWNGJy1GZW42JC1GIzYnLUZSNiVRIiVGJ0ZgcUZhcS1GODYtUSIsRidGNEY7RmpwRkBGQkZERkZGSEZKL0ZOUSwwLjMzMzMzMzNlbUYnLUYxNiRRIjZGJ0Y0Rl9vRjRGNEZfb0Y0LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2JVElZXZhbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUYsNiVRI1QyRidGL0YyLUY2NiQtRiM2JC1JI21uR0YkNiRRIjVGJy9GM1Enbm9ybWFsRidGRUZFLUkjbW9HRiQ2LVEiLEYnRkUvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGTS8lKnN5bW1ldHJpY0dGTS8lKGxhcmdlb3BHRk0vJS5tb3ZhYmxlbGltaXRzR0ZNLyUnYWNjZW50R0ZNLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRi9GMi1GSDYtUSI9RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GYm8tRkI2JFEkMC41RidGRUZFRkUtRkg2LVEiOkYnRkVGS0Zgb0ZQRlJGVEZWRlhGYW9GY28tRiw2JVEmZXZhbGZGJ0YvRjItRjY2JC1GIzYnLUYsNiVRIiVGJ0YvRjJGRy1GQjYkUSI2RidGRS8lK2V4ZWN1dGFibGVHRk1GRUZFLUZINi1RIjtGJ0ZFRktGTkZQRlJGVEZWRlhGWkZjby1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0Zmbi8lJmRlcHRoR0ZhcS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GXXE2JkZfcUZicUZkcS9GZ3FRJWF1dG9GJ0YrLUY2NiQtRiM2KUY6LUY2NiQtRiM2JEZkcEZFRkVGR0ZqbkZdb0Zkb0ZFRkVGZ29Gam8tRjY2JC1GIzYmRmFwRkdGZHBGRUZFRmdwRkU=The 12th degree Taylor polynomial is the first which rounds off correctly to 7 decimal places.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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5LyUrZXhlY3V0YWJsZUdGPUY5 means: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The pendulum sreaches the upward vertical direction. If it goes beyond, it does not oscillate about the downward vertical direction any more since it tcontinues rotating around forever. The upward direction is in fact an unstable 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limit at 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lowest order (power) terms in the numerator and denominator are the same so the quotient of their coefficients is the 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