MAT2500-05 22f Quiz 6 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 if appropriate). Indicate where technology is used and what type (Maple, GC). Only use technology to CHECK hand calculations, not substitute for them.1. Suppose we compare the area of the European letter size A4 dimensions of 21.0x29.7 cm to our American standard letter size 8.5x11 in. [Recall 1in = 2.54 cm.]
a) Letting 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evaluate the differentials of the dimensions of the A4 size paper compared with our letter size dimensions, and use the differential approximation to evaluate the approximate change in area and its fractional (and percentage) change.
b) Then compare this approximate change in area with the exact such change in the area: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEjZEFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RKCZtaW51cztGJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk4tRiw2JlEoJiM5MTY7QUYnRi9GMkY1RjJGPA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiLkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYvc) Use the linear approximation to the ratio of vertical to horizontal dimension to evaluate the approximate ratio of the European A4 dimensions, and compare to the actual ratio (evaluate the difference over the actual ratio). 2. Error Analysis.
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The volume formula is 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
If these measurements are only known to be accurate to the nearest foot, what is the maximum absolute error in the computed volume using the differential approximation? How does that compare to the exact change if we evaluate the exact volume at the upper end of the error bar for each dimension? [Hint: which is the interval around each measurement that allows them to be "to the nearest foot"?]solution1. inches (more natural since we are Americans!)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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The old and new dimensions and their differentials: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Exact area and dimension ratios: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 differential approximation is about 5 % higher than the actual change in the area.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The linear approximation is about .1 percent lower than the exact value of the dimension ratio.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JSFH1. 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The old and new dimensions and their differentials: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 area and dimension ratios: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The differential approximation is about 5 % higher than the actual change in the area.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEjZEFGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ki1GRzYlUSNYMEYnRkpGTS1GLDYtUSIsRidGL0YyL0Y2RkxGN0Y5RjtGPUY/RkEvRkVRLDAuMzMzMzMzM2VtRictRkc2JVEjWTBGJ0ZKRk1GVy1GRzYlUSdkZWx0YXhGJ0ZKRk1GVy1GRzYlUSdkZWx0YXlGJ0ZKRk1GL0YvLUYsNi1RIjtGJ0YvRjJGWkY3RjlGO0Y9Rj9GQS9GRVEsMC4yNzc3Nzc4ZW1GJ0YrLUkmbWZyYWNHRiQ2KC1GIzYmRkZGTy8lK2V4ZWN1dGFibGVHRjRGLy1GIzYnRistRkc2JVEiQUYnRkpGTS1GUDYkLUYjNiZGVEZXRmduRi9GL0ZKRk0vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmpwLyUpYmV2ZWxsZWRHRjRGYG9GKy1GRzYlUSdkZWx0YUFGJ0ZKRk1GYG8tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGQy8lJmRlcHRoR0ZncS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GY3E2JkZlcUZocUZqcS9GXXJRJWF1dG9GJ0ZGRk8tRiw2LVEoJm1pbnVzO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yMjIyMjIyZW1GJy9GRUZnckZfcUZgby1GZm82KC1GIzYoRkZGT0ZjckZfcUZqb0YvLUYjNidGX3FGSi8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnLyUscGxhY2Vob2xkZXJHRkxGTUZlcEZocEZbcUZdcUZqb0YvJSFHThe linear approximation is about .1 percent lower than the exact value of the dimension ratio.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYyLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRIlhGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRIllGJ0YvRjIvJStleGVjdXRhYmxlR0ZFRkFGQS1GPjYtUSI7RidGQUZDRkZGSEZKRkxGTkZQRlIvRlZRLDAuMjc3Nzc3OGVtRictRiw2JVEjTFJGJ0YvRjItRjY2JC1GIzYrRjpGPUZYRj0tRiw2JVEjWDBGJ0YvRjJGPS1GLDYlUSNZMEYnRi9GMkZlbkZBRkFGZ24tRj42LVEifkYnRkFGQy9GR0ZFRkhGSkZMRk5GUEZSL0ZWRlRGXG8tRjY2JC1GIzYqRjpGPUZYRj1GY29GPUZmb0ZBRkEtRj42LVEoJm1pbnVzO0YnRkFGQ0ZccEZIRkpGTEZORlAvRlNRLDAuMjIyMjIyMmVtRicvRlZGZnBGKy1GNjYkLUYjNiZGOkY9RlhGQUZBRmduLUkmbWZyYWNHRiQ2KC1GIzYoRlxvRl5wRmJwRitGaHBGQS1GIzYmRitGaHBGL0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZocS8lKWJldmVsbGVkR0ZFRmVuRkE=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYvLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSJSRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEieEYnRjRGNy1JI21vR0YkNi1RIixGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGSi8lKnN5bW1ldHJpY0dGSi8lKGxhcmdlb3BHRkovJS5tb3ZhYmxlbGltaXRzR0ZKLyUnYWNjZW50R0ZKLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieUYnRjRGN0ZGRkZGQi1GLDYlUSNMUkYnRjRGNy1GOzYkLUYjNipGP0ZCRmduRkItRiw2JVEjWDBGJ0Y0RjdGQi1GLDYlUSNZMEYnRjRGN0ZGRkZGRkYrLyUrZXhlY3V0YWJsZUdGSkZGLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGPUZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoZGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYrLUYsNiVRLHBvaW50cGxvdDNkRidGL0YyLUY2NiQtRiM2Ni1GNjYmLUYjNictRjY2Ji1GIzYqLUYsNiVRI1gwRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZULyUqc3ltbWV0cmljR0ZULyUobGFyZ2VvcEdGVC8lLm1vdmFibGVsaW1pdHNHRlQvJSdhY2NlbnRHRlQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSNZMEYnRi9GMkZMLUYsNiVRIlJGJ0YvRjItRjY2JC1GIzYnRklGTEZhby8lK2V4ZWN1dGFibGVHRlRGUEZQRltwRlBGUC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZMLUY2NiYtRiM2Ki1GLDYlUSJYRidGL0YyRkwtRiw2JVEiWUYnRi9GMkZMRmRvLUY2NiQtRiM2J0ZncEZMRmpwRltwRlBGUEZbcEZQRlBGXXBGYHBGW3BGUEZQRl1wRmBwRkwtRiw2JVEmc3R5bGVGJ0YvRjItRk02LVEiPUYnRlBGUi9GVkZURldGWUZlbkZnbkZpbi9GXG9RLDAuMjc3Nzc3OGVtRicvRl9vRmlxLUYsNiVRJnBvaW50RidGL0YyRkwtRiw2JVEnc3ltYm9sRidGL0YyRmRxLUYsNiVRLHNvbGlkc3BoZXJlRidGL0YyRkwtRk02LVEifkYnRlBGUkZncUZXRllGZW5GZ25GaW5GW28vRl9vRl1vLUYsNiVRK3N5bWJvbHNpemVGJ0YvRjJGZHEtSSNtbkdGJDYkUSMxNUYnRlBGTC1GLDYlUSZjb2xvckYnRi9GMkZkcS1GNjYmLUYjNictRiw2JVEkcmVkRidGL0YyRkwtRiw2JVElYmx1ZUYnRi9GMkZbcEZQRlBGXXBGYHBGW3BGUEZQRkwtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGXW8vJSZkZXB0aEdGYXQvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRl10NiZGX3RGYnRGZHQvRmd0USVhdXRvRictRiw2JVEncGxvdDNkRidGL0YyLUY2NiQtRiM2NC1GNjYmLUYjNihGZG8tRjY2JC1GIzYmLUYsNiVRInhGJ0YvRjJGTC1GLDYlUSJ5RidGL0YyRlBGUEZMLUYsNiVRI0xSRidGL0YyLUY2NiQtRiM2KkZcdkZMRl92RkxGSUZMRmFvRlBGUEZQRlBGXXBGYHBGTEZcdkZkcS1GXHM2JFElOC4yN0YnRlAtRk02LVEjLi5GJ0ZQRlJGZ3FGV0ZZRmVuRmduRmluL0Zcb1EsMC4yMjIyMjIyZW1GJ0Znci1GXHM2JFEkOC41RidGUEZMRl92RmRxLUZcczYkUSUxMS4wRidGUEZcdy1GXHM2JFElMTEuN0YnRlBGTEZhcUZkcS1GNjYmLUYjNiYtRiw2JVExU3VyZmFjZVdpcmVmcmFtZUYnRi9GMkZMLUYsNiVRL1N1cmZhY2VDb250b3VyRidGL0YyRlBGUEZdcEZgcEZQRlBGW3BGUEZQRltwRlA=2.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fractional error in the increment estimate compared to the actual maximum increment of the error bar is on the order of less than 1 percent.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv