MAT1505-03/04 17F Final Exam 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).p1. The cochleoid described by the polar equation 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 spirals into the origin with an infinite series of loops. a) Set up a fully simplified integral for the arclength LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn of the loop LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtaUdGJDYlUSUmcGk7RicvJSdpdGFsaWNHRjRGLy1GLDYtUSYmbGVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZQLUZHNiVRJyYjOTUyO0YnRkpGL0ZMRkYvJStleGVjdXRhYmxlR0Y0Ri8= , and evaluate it numerically to 4 digit accuracy. This is an improper integral. Why? Plot its integrand over this interval to confirm that it is well behaved (continuous) on that interval and give a rough sketch, labeling axes and tickmarks.
[Optional: 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. Expand LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEmbnVtZXJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRInRGJ0YvRjJGNUYyL0Y2USdub3JtYWxGJ0YyRkBGMkZA in a Taylor series at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy1JI21uR0YkNiVRIjBGJ0YyRjRGMkY0 to evaluate 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; helpful: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].b) Set up a definite integral for the area enclosed by the cochleoid loop 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 , exactly and then to 4 significant digit accuracy.c) Make a rough sketch of this curve segment together with the inscribed circle 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 , and compare your previous results with the area and circumference of this circle. Are they reasonable? [Be sure to include tickmarks labeling your axes in your sketch. Remember the formulas for the circumference and area of a circle!]d) Write down in simplest form the equation whose solution determines the angle 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 in the first quadrant where the tangent line is horizontal, and solve it numerically to 10 digit accuracy and evaluate the Cartesian coordinates of this point to 4 digit accuracy.2. The right strophoid 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 traces out the curve 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 with the graph 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 corresponding to the one half of this curve.a) Make a rough sketch of this curve for 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. Annotate the key points (endpoints and axis intercepts) you see with the values of 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 and put an arrowhead on each segment of the curve indicating increasing values of its parameter.b) What is the limit of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn as 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? What does this tell you about the asymptotic behavior of the curve?c) Evaluate the slopes of the tangent lines of the points on this parametrized curve which pass through the origin. What (smallest) angles 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 do these slopes 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 correspond to?d) For what interval is the closed loop portion of this curve traced out? What interval corresponds to the upper half of the loop? Evaluate the exact area of this loop using its parametric representation (state the simplified integral you evaluate) and give its numerical value to 4 decimal places.e) Evaluate the exact area of the loop by doubling the area of the upper half of the loop obtained using its equation as a graph of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn versus LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn and give its numerical value to 4 decimal places.f) Since 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, it is relatively straightforward to convert the Cartesian equation of this curve to the polar coordinate form
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. At what values of 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 does this pass through the origin?
Evaluate the area of the inner loop using this polar form of the curve and compare its exact value with the results of part d) and e).
f) Optional. Show that the parametrized curve satisfies the given Cartesian equation of this curve. Derive the polar form of the Cartesian form of this curve.solution1. 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 polar plot was not intended but does work to understand the limit at zero angle.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you try to do this integral instead, it differs in sign from the extra terms, because of the counterclockwise loop.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbWlHRiQ2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIn5GJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVi1GLDYlUSJYRidGL0YyLUZDNi1RIidGJ0ZARkZGSEZKRkxGTkZQRlIvRlVRLDAuMTExMTExMWVtRidGV0Y1LUZDNi1RIjtGJ0ZARkYvRklGMUZKRkxGTkZQRlJGVC9GWFEsMC4yNzc3Nzc4ZW1GJy1GLDYlUSlzaW1wbGlmeUYnRi9GMi1GNjYkLUYjNiUtRiw2JVEiJUYnRi9GMkY9RkBGQEZbby1GQzYtUSomdW1pbnVzMDtGJ0ZARkZGSEZKRkxGTkZQRlIvRlVRLDAuMjIyMjIyMmVtRicvRlhGX3AtSSNtbkdGJDYkUSIyRidGQC1JKG1zdWJzdXBHRiQ2Jy1GQzYtUSsmSW50ZWdyYWw7RidGQEZGRkgvRktGMUZML0ZPRjFGUEZSRlRGVy1GIzYnLUZicDYkUSIwRidGQEYvLyUrZm9yZWdyb3VuZEdRLFsyMDAsMCwyMDBdRicvJSxwbGFjZWhvbGRlckdGMUYyLUYjNictRiw2JVElJnBpO0YnL0YwRj9GQEYvRmJxRmVxRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZhcS8lL3N1YnNjcmlwdHNoaWZ0R0ZhcUZob0ZCLUZDNi1RMCZEaWZmZXJlbnRpYWxEO0YnRkAvRkdRJnVuc2V0RicvRklGZXIvRktGZXIvRk1GZXIvRk9GZXIvRlFGZXIvRlNGZXJGVEZXRjpGPUZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSZtZnJhY0dGJDYoLUYjNiotSSVtc3VwR0YkNiUtRiM2Ki1JI21pR0YkNiVRJHNpbkYnLyUnaXRhbGljR0Y0Ri8tRiw2LVEwJkFwcGx5RnVuY3Rpb247RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFRlotSShtZmVuY2VkR0YkNiQtRlE2JVEidEYnL0ZVUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8vJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRicvJStleGVjdXRhYmxlR0Y0LyUpcmVhZG9ubHlHRl1vLyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RidGLy1JI21uR0YkNiRRIjJGJ0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGL0YyRjVGN0Y5RjtGPUY/RllGZW4tRmduNiQtRiM2LC1GIzYsRmpvRmFwLUZMNiUtRiM2Ki1GUTYlUSRjb3NGJ0ZURi9GVkZmbkZgb0Zjb0Zlb0Znb0YvRmpvRl5wRmFwRmluRmBvRmNvRmVvRmdvRi8tRiw2LVEoJm1pbnVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRiM2KkZccUZhcEZORmBvRmNvRmVvRmdvRi9GYXFGaW5GYG9GY29GZW9GZ29GL0YvRmBvRmNvRmVvRmdvRi8tRkw2JUZpbi1GW3A2JFEiM0YnRi9GXnAvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmByLyUpYmV2ZWxsZWRHRjQtRiw2LVEiPUYnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZpci1GUTYlUSdleHBhbmRGJ0Zcb0Zeby1GZ242JC1GIzYmRitGRkZjb0YvRi9GY29GLw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkobXN1YnN1cEdGJDYnLUkjbW9HRiQ2LVErJkludGVncmFsO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZHLUYjNiUtRi82LVEqJnVtaW51czA7RidGMi9GNlEmZmFsc2VGJy9GOUZQL0Y7RlAvRj5GUC9GQEZQL0ZCRlAvRkRGUC9GRlEsMC4yMjIyMjIyZW1GJy9GSUZYLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR0ZQRjJGMi1GIzYkRlpGMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJS9zdWJzY3JpcHRzaGlmdEdGXm8tRmVuNiNRIUYnLUkmbWZyYWNHRiQ2KC1GIzYmLUYvNi1RIn5GJ0YyRk9GUUZSRlNGVEZVRlZGRUZILUZlbjYlUSRzaW5GJ0ZobkYyLUklbXN1cEdGJDYlLUkobWZlbmNlZEdGJDYkLUZlbjYlUSJ0RicvRmluRjwvRjNRJ2l0YWxpY0YnRjItSSNtbkdGJDYkUSIyRidGMkZcb0YyLUZgcDYlRmVwLUYjNiVGW3FGaHBGaXBGXG8vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmhxLyUpYmV2ZWxsZWRHRlBGaW8tRi82LVEwJkRpZmZlcmVudGlhbEQ7RidGMkY1RjgvRjtGN0Y9L0ZARjdGQUZDRkVGSEZlcC1GLzYtUSI7RidGMkZPL0Y5RjxGUkZTRlRGVUZWRkUvRklRLDAuMjc3Nzc3OGVtRictRiw2Jy1GLzYtRjFGMkZPRlFGOkZTRj9GVUZWRkVGSC1GIzYoRkxGWkZocC8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnLyUscGxhY2Vob2xkZXJHRjxGaXAtRiM2J0ZaRmhwRl5zRmFzRmlwRlxvRl9vRkwtRmVvNigtRiM2LEZbcS1GLzYtUTEmSW52aXNpYmxlVGltZXM7RidGMkZPRlFGUkZTRlRGVUZWRkVGSC1GYHA2JS1GIzYqRlxwLUYvNi1RMCZBcHBseUZ1bmN0aW9uO0YnRjJGT0ZRRlJGU0ZURlVGVkZFRkhGYnAvRl9zUSpbMCwwLDI1NV1GJy8lK2V4ZWN1dGFibGVHRlAvJSlyZWFkb25seUdGPC8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYnRjJGW3FGXG9GaXMtRmBwNiUtRiM2Ki1GZW42JVEkY29zRidGaG5GMkZgdEZicEZjdEZldEZndEZpdEYyRltxRlxvRmN0RmV0Rmd0Rml0RjItRmBwNiVGZXBGW3FGXG9GY3FGZnFGaXFGW3ItRi82LVEnJnBsdXM7RidGMkZPRlFGUkZTRlRGVUZWRldGWS1GZW82KC1GIzYqLUZgcDYlRl50LUZccTYkUSIzRidGMkZcb0Zpc0ZedUZjdEZldEZndEZpdEYyLUZgcDYlRmVwRl52RlxvRmNxRmZxRmlxRltyRmlvRl1yRmVwRmV0RjI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY5LUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGMi1GIzYlLUZQNiRRIjJGJ0YyL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnLyUubGluZXRoaWNrbmVzc0dGUi8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zqbi8lKWJldmVsbGVkR0YxLUY2Ni1RIn5GJ0YyRjlGO0Y9Rj9GQUZDRkUvRkhRJjAuMGVtRicvRktGY28tRiw2JVEkdGFuRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiVGKy8lK2V4ZWN1dGFibGVHRjFGMkYyLUY2Ni1RIjtGJ0Y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are more inner curls...interesting.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. right 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degrees with respect to the 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agrees with the 45 degree slope lines at the origin.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State_341163930_5864_47763753938_0
Optional: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JSFHunused Stewart 10.R.29 parametrized curve areaa) Make a rough sketch of the parametrized curve 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 , indicating the direction of increasing parameter values.b) Find the three points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUSJ5RidGNEY3RjpGN0ZBRjdGQUY3RkE= on this parametrized curve where the tangent lines are either horizontal or vertical. c) One of the points with a vertical tangent is a point of self-intersection of the curve for two values 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 of the parameter. Evaluate (by hand) 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 for the loop this self-intersection creates to find the exact area LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn it encloses. Does its value seem consistent with your sketch? Try to support your response with some kind of estimate for this area.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polar coordinate area problem between two curvesJSFHInside 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 and outside 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GJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GXW8tRiw2JVEkc2luRidGUkY5LUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEoJnRoZXRhO0YnRlJGOUY5RjlGOS1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHRj1GOQ==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unused Stewart 10.R.40. generalized to sequence of even powers of cosine, 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=unused Stewart 10.R.58. parametrized curve. folium of 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Evaluate the integral LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkobXN1YnN1cEdGJDYnLUkjbW9HRiQ2LVErJkludGVncmFsO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZHLUYjNiQtSSNtbkdGJDYkUSIwRidGMkYyLUYjNiQtRi82LVEoJmluZmluO0YnRjIvRjZRJmZhbHNlRicvRjlGVi9GO0ZWL0Y+RlYvRkBGVi9GQkZWL0ZERlZGRUZIRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZPLyUvc3Vic2NyaXB0c2hpZnRHRk8tSSZtZnJhY0dGJDYoLUYjNiotRk02JFEiM0YnRjItRi82LVExJkludmlzaWJsZVRpbWVzO0YnRjJGVUZXRlhGWUZaRmVuRmZuRkVGSC1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYyLUZnbzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR0Y8L0YzUSdpdGFsaWNGJy1GTTYkUSI4RidGMkZnbi1GLzYtUScmcGx1cztGJ0YyRlVGV0ZYRllGWkZlbkZmbi9GRlEsMC4yMjIyMjIyZW1GJy9GSUZfcS1GIzYqLUZNNiRRIjRGJ0YyRmNvLUZnbzYlRmBwLUZNNiRRIjZGJ0YyRmduLyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYnLyUrZXhlY3V0YWJsZUdGVi8lKXJlYWRvbmx5R0Y8LyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RidGMi1GLzYtUSgmbWludXM7RidGMkZVRldGWEZZRlpGZW5GZm5GXnFGYHEtRiM2KkZjcUZjby1GZ282JUZgcC1GTTYkUSI1RidGMkZnbkZbckZeckZgckZickYyRmVyLUYjNipGY3FGY28tRmdvNiVGYHBGYG9GZ25GW3JGXnJGYHJGYnJGMkZbcS1GIzYqRmNxRmNvLUZnbzYlRmBwLUZNNiRRIjJGJ0YyRmduRltyRl5yRmByRmJyRjJGW3EtRk02JFEiMUYnRjJGW3JGXnJGYHJGYnJGMkYyLUYjNiUtRlxvNihGanMtRiM2JUZnc0ZkcEZmcC8lLmxpbmV0aGlja25lc3NHRlx0LyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmd0LyUpYmV2ZWxsZWRHRlZGZHBGZnBGZ25GW3JGXnJGYHJGYnJGMi1GZ282JS1Gam82JC1GIzYqRmFzRltxRmpzRltyRl5yRmByRmJyRjJGMkZhdEZnbkZjdEZldEZodEZqdC1GLzYtUSJ+RidGMkZVRldGWEZZRlpGZW5GZm5GRUZILUYvNi1RMCZEaWZmZXJlbnRpYWxEO0YnRjJGNUY4L0Y7RjdGPS9GQEY3RkFGQ0ZFRkhGYHAtRi82LVEiO0YnRjJGVS9GOUY8RlhGWUZaRmVuRmZuRkUvRklRLDAuMjc3Nzc3OGVtRictRmFwNiVRJmV2YWxmRidGZHBGZnAtRmpvNiQtRiM2JS1GYXA2JVEiJUYnRmRwRmZwRl5yRjJGMkZeckYyLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRkAtRiM2JC1JI21uR0YkNiRRIjJGJ0ZARkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiK0YnRkAvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlEvJSlzdHJldGNoeUdGUS8lKnN5bW1ldHJpY0dGUS8lKGxhcmdlb3BHRlEvJS5tb3ZhYmxlbGltaXRzR0ZRLyUnYWNjZW50R0ZRLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGam5GKy1GTDYtUSInRidGQEZPRlJGVEZWRlhGWkZmbi9GaW5RLDAuMTExMTExMWVtRicvRlxvUSYwLjBlbUYnRjUtRkw2LVEiO0YnRkBGTy9GU0YxRlRGVkZYRlpGZm4vRmluRmNvL0Zcb1EsMC4yNzc3Nzc4ZW1GJy1GLDYlUSlzaW1wbGlmeUYnRi9GMi1GOTYkLUYjNiQtRiw2JVEiJUYnRi9GMkZARkBGZG8tSSZtZnJhY0dGJDYoLUYjNiYtRiw2JVEmbnVtZXJGJ0YvRjItRjk2JC1GIzYlRmJwLyUrZXhlY3V0YWJsZUdGUUZARkBGYXFGQC1GIzYlLUZFNiRRIjlGJ0ZARi9GMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXXIvJSliZXZlbGxlZEdGUUZhcUZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=unused Stewart 10.R.27,28. parametrized curve. another 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Remember for a single parametrized curve, or a pair of polar coordinate curves: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: " " (space) or "*" for multiplication ALWAYS, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSUmbmU7RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy1GLDYmUSNwaUYnRi9GMkY0RjJGNA==, 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 .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: M7R0
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